diff --git a/src/transformers/modeling_t5.py b/src/transformers/modeling_t5.py
index 5235629c60..9ac085495f 100644
--- a/src/transformers/modeling_t5.py
+++ b/src/transformers/modeling_t5.py
@@ -16,7 +16,6 @@
 
 
 import copy
-import itertools
 import logging
 import math
 import os
@@ -185,13 +184,11 @@ class T5LayerFF(nn.Module):
 
 
 class T5Attention(nn.Module):
-    NEW_ID = itertools.count()
-
     def __init__(self, config, has_relative_attention_bias=False):
         super().__init__()
-        self.layer_id = next(T5Attention.NEW_ID)
         self.is_decoder = config.is_decoder
         self.has_relative_attention_bias = has_relative_attention_bias
+        self.output_past = config.output_past
 
         self.output_attentions = config.output_attentions
         self.relative_attention_num_buckets = config.relative_attention_num_buckets
@@ -294,15 +291,37 @@ class T5Attention(nn.Module):
         values = values.permute([2, 0, 1]).unsqueeze(0)  # shape (1, num_heads, qlen, klen)
         return values
 
-    def forward(self, input, mask=None, kv=None, position_bias=None, cache=None, head_mask=None):
+    def forward(
+        self,
+        input,
+        mask=None,
+        kv=None,
+        position_bias=None,
+        past_key_value_state=None,
+        head_mask=None,
+        query_length=None,
+    ):
         """
         Self-attention (if kv is None) or attention over source sentence (provided by kv).
         """
         # Input is (bs, qlen, dim)
         # Mask is (bs, klen) (non-causal) or (bs, klen, klen)
+        # past_key_value_state[0] is (bs, n_heads, q_len - 1, dim_per_head)
         bs, qlen, dim = input.size()
+
+        if past_key_value_state is not None:
+            assert self.is_decoder is True, "Encoder cannot cache past key value states"
+            assert (
+                len(past_key_value_state) == 2
+            ), "past_key_value_state should have 2 past states: keys and values. Got {} past states".format(
+                len(past_key_value_state)
+            )
+            real_qlen = qlen + past_key_value_state[0].shape[2] if query_length is None else query_length
+        else:
+            real_qlen = qlen
+
         if kv is None:
-            klen = qlen if cache is None else cache["slen"] + qlen
+            klen = real_qlen
         else:
             klen = kv.size(1)
 
@@ -315,23 +334,27 @@ class T5Attention(nn.Module):
             return x.transpose(1, 2).contiguous().view(bs, -1, self.inner_dim)
 
         q = shape(self.q(input))  # (bs, n_heads, qlen, dim_per_head)
+
         if kv is None:
             k = shape(self.k(input))  # (bs, n_heads, qlen, dim_per_head)
             v = shape(self.v(input))  # (bs, n_heads, qlen, dim_per_head)
-        elif cache is None or self.layer_id not in cache:
+        elif past_key_value_state is None:
             k = v = kv
             k = shape(self.k(k))  # (bs, n_heads, qlen, dim_per_head)
             v = shape(self.v(v))  # (bs, n_heads, qlen, dim_per_head)
 
-        if cache is not None:
-            if self.layer_id in cache:
-                if kv is None:
-                    k_, v_ = cache[self.layer_id]
-                    k = torch.cat([k_, k], dim=2)  # (bs, n_heads, klen, dim_per_head)
-                    v = torch.cat([v_, v], dim=2)  # (bs, n_heads, klen, dim_per_head)
-                else:
-                    k, v = cache[self.layer_id]
-            cache[self.layer_id] = (k, v)
+        if past_key_value_state is not None:
+            if kv is None:
+                k_, v_ = past_key_value_state
+                k = torch.cat([k_, k], dim=2)  # (bs, n_heads, klen, dim_per_head)
+                v = torch.cat([v_, v], dim=2)  # (bs, n_heads, klen, dim_per_head)
+            else:
+                k, v = past_key_value_state
+
+        if self.is_decoder and self.output_past:
+            present_key_value_state = ((k, v),)
+        else:
+            present_key_value_state = (None,)
 
         # q = q / math.sqrt(dim_per_head)                                     # No scaling in T5
         scores = torch.einsum("bnqd,bnkd->bnqk", q, k)  # (bs, n_heads, qlen, klen)
@@ -339,7 +362,13 @@ class T5Attention(nn.Module):
         if position_bias is None:
             if not self.has_relative_attention_bias:
                 raise ValueError("No position_bias provided and no weights to compute position_bias")
-            position_bias = self.compute_bias(qlen, klen)
+            position_bias = self.compute_bias(real_qlen, klen)
+
+            # if key and values are already calculated
+            # we want only the last query position bias
+            if past_key_value_state is not None:
+                position_bias = position_bias[:, :, -1:, :]
+
             if mask is not None:
                 position_bias = position_bias + mask  # (bs, n_heads, qlen, klen)
 
@@ -357,6 +386,13 @@ class T5Attention(nn.Module):
         context = self.o(context)
 
         outputs = (context,)
+
+        if self.output_past is False or self.is_decoder is False:
+            assert (
+                present_key_value_state[0] is None
+            ), "Key/Value projections should not be stored if {} is not decoder or output_past is False".format(self)
+
+        outputs = outputs + present_key_value_state
         if self.output_attentions:
             outputs = outputs + (weights,)
         if self.has_relative_attention_bias:
@@ -371,10 +407,16 @@ class T5LayerSelfAttention(nn.Module):
         self.layer_norm = T5LayerNorm(config.d_model, eps=config.layer_norm_epsilon)
         self.dropout = nn.Dropout(config.dropout_rate)
 
-    def forward(self, hidden_states, attention_mask=None, position_bias=None, head_mask=None):
+    def forward(
+        self, hidden_states, attention_mask=None, position_bias=None, head_mask=None, past_key_value_state=None
+    ):
         norm_x = self.layer_norm(hidden_states)
         attention_output = self.SelfAttention(
-            norm_x, mask=attention_mask, position_bias=position_bias, head_mask=head_mask
+            norm_x,
+            mask=attention_mask,
+            position_bias=position_bias,
+            head_mask=head_mask,
+            past_key_value_state=past_key_value_state,
         )
         y = attention_output[0]
         layer_output = hidden_states + self.dropout(y)
@@ -389,10 +431,25 @@ class T5LayerCrossAttention(nn.Module):
         self.layer_norm = T5LayerNorm(config.d_model, eps=config.layer_norm_epsilon)
         self.dropout = nn.Dropout(config.dropout_rate)
 
-    def forward(self, hidden_states, kv, attention_mask=None, position_bias=None, head_mask=None):
+    def forward(
+        self,
+        hidden_states,
+        kv,
+        attention_mask=None,
+        position_bias=None,
+        head_mask=None,
+        past_key_value_state=None,
+        query_length=None,
+    ):
         norm_x = self.layer_norm(hidden_states)
         attention_output = self.EncDecAttention(
-            norm_x, mask=attention_mask, kv=kv, position_bias=position_bias, head_mask=head_mask
+            norm_x,
+            mask=attention_mask,
+            kv=kv,
+            position_bias=position_bias,
+            head_mask=head_mask,
+            past_key_value_state=past_key_value_state,
+            query_length=query_length,
         )
         y = attention_output[0]
         layer_output = hidden_states + self.dropout(y)
@@ -403,14 +460,14 @@ class T5LayerCrossAttention(nn.Module):
 class T5Block(nn.Module):
     def __init__(self, config, has_relative_attention_bias=False):
         super().__init__()
+        self.output_past = config.output_past
         self.is_decoder = config.is_decoder
         self.layer = nn.ModuleList()
         self.layer.append(T5LayerSelfAttention(config, has_relative_attention_bias=has_relative_attention_bias))
         if self.is_decoder:
             self.layer.append(T5LayerCrossAttention(config, has_relative_attention_bias=has_relative_attention_bias))
-            self.layer.append(T5LayerFF(config))
-        else:
-            self.layer.append(T5LayerFF(config))
+
+        self.layer.append(T5LayerFF(config))
 
     def forward(
         self,
@@ -421,31 +478,63 @@ class T5Block(nn.Module):
         encoder_attention_mask=None,
         encoder_decoder_position_bias=None,
         head_mask=None,
+        past_key_value_state=None,
     ):
-        self_attention_outputs = self.layer[0](
-            hidden_states, attention_mask=attention_mask, position_bias=position_bias, head_mask=head_mask
-        )
-        hidden_states = self_attention_outputs[0]
-        outputs = self_attention_outputs[1:]  # Keep self-attention outputs and relative position weights
 
-        if not self.is_decoder:
-            hidden_states = self.layer[1](hidden_states)
+        if past_key_value_state is not None:
+            assert self.is_decoder, "Only decoder can use `past_key_value_states`"
+            assert (
+                len(past_key_value_state) == 4
+            ), "The should be 4 past states. 2 (past / key) for self attention. 2 (past / key) for cross attention. Got {} past key / value states".format(
+                len(past_key_value_state)
+            )
+            self_attn_past_key_value_state = past_key_value_state[:2]
+            cross_attn_past_key_value_state = past_key_value_state[2:]
         else:
+            self_attn_past_key_value_state, cross_attn_past_key_value_state = None, None
+
+        self_attention_outputs = self.layer[0](
+            hidden_states,
+            attention_mask=attention_mask,
+            position_bias=position_bias,
+            head_mask=head_mask,
+            past_key_value_state=self_attn_past_key_value_state,
+        )
+        hidden_states, present_key_value_state = self_attention_outputs[:2]
+        attention_outputs = self_attention_outputs[2:]  # Keep self-attention outputs and relative position weights
+
+        if self.is_decoder:
+            # the actual query length is unknown for cross attention
+            # if using past key value states. Need to inject it here
+            if present_key_value_state is not None:
+                query_length = present_key_value_state[0].shape[2]
+            else:
+                query_length = None
+
             cross_attention_outputs = self.layer[1](
                 hidden_states,
                 kv=encoder_hidden_states,
                 attention_mask=encoder_attention_mask,
                 position_bias=encoder_decoder_position_bias,
                 head_mask=head_mask,
+                past_key_value_state=cross_attn_past_key_value_state,
+                query_length=query_length,
             )
             hidden_states = cross_attention_outputs[0]
-            outputs = (
-                outputs + cross_attention_outputs[1:]
-            )  # Keep cross-attention outputs and relative position weights
-            hidden_states = self.layer[2](hidden_states)
+            # Combine self attn and cross attn key value states
+            if present_key_value_state is not None:
+                present_key_value_state = present_key_value_state + cross_attention_outputs[1]
 
-        outputs = (hidden_states,) + outputs  # add attentions if we output them
-        return outputs  # hidden-states, (self-attention weights), (self-attention position bias), (cross-attention weights), (cross-attention position bias)
+            # Keep cross-attention outputs and relative position weights
+            attention_outputs = attention_outputs + cross_attention_outputs[2:]
+
+        # Apply Feed Forward layer
+        hidden_states = self.layer[-1](hidden_states)
+        outputs = (hidden_states,)
+
+        # Add attentions if we output them
+        outputs = outputs + (present_key_value_state,) + attention_outputs
+        return outputs  # hidden-states, present_key_value_states, (self-attention weights), (self-attention position bias), (cross-attention weights), (cross-attention position bias)
 
 
 class T5PreTrainedModel(PreTrainedModel):
@@ -531,6 +620,7 @@ class T5Stack(T5PreTrainedModel):
 
         self.embed_tokens = embed_tokens
         self.is_decoder = config.is_decoder
+        self.output_past = config.output_past and self.is_decoder
 
         self.block = nn.ModuleList(
             [T5Block(config, has_relative_attention_bias=bool(i == 0)) for i in range(config.num_layers)]
@@ -557,6 +647,7 @@ class T5Stack(T5PreTrainedModel):
         encoder_attention_mask=None,
         inputs_embeds=None,
         head_mask=None,
+        past_key_value_states=None,
     ):
 
         if input_ids is not None and inputs_embeds is not None:
@@ -575,25 +666,41 @@ class T5Stack(T5PreTrainedModel):
 
         batch_size, seq_length = input_shape
 
+        if past_key_value_states is not None:
+            assert seq_length == 1, "Input shape is {}, but should be {} when using past_key_value_sates".format(
+                input_shape, (batch_size, 1)
+            )
+            # required mask seq length can be calculated via length of past
+            # key value states and seq_length = 1 for the last token
+            mask_seq_length = past_key_value_states[0][0].shape[2] + seq_length
+        else:
+            mask_seq_length = seq_length
+
         if attention_mask is None:
-            attention_mask = torch.ones(batch_size, seq_length).to(inputs_embeds.device)
-        if self.is_decoder and encoder_attention_mask is None:
+            attention_mask = torch.ones(batch_size, mask_seq_length).to(inputs_embeds.device)
+        if self.is_decoder and encoder_attention_mask is None and encoder_hidden_states is not None:
             encoder_seq_length = encoder_hidden_states.shape[1]
             encoder_attention_mask = torch.ones(batch_size, encoder_seq_length).to(inputs_embeds.device)
 
+        # initialize past_key_value_states with `None` if past does not exist
+        if past_key_value_states is None:
+            past_key_value_states = [None] * len(self.block)
+
         # We can provide a self-attention mask of dimensions [batch_size, from_seq_length, to_seq_length]
         # ourselves in which case we just need to make it broadcastable to all heads.
         if attention_mask.dim() == 3:
             extended_attention_mask = attention_mask[:, None, :, :]
         elif attention_mask.dim() == 2:
-            # Provided a padding mask of dimensions [batch_size, seq_length]
+            # Provided a padding mask of dimensions [batch_size, mask_seq_length]
             # - if the model is a decoder, apply a causal mask in addition to the padding mask
-            # - if the model is an encoder, make the mask broadcastable to [batch_size, num_heads, seq_length, seq_length]
+            # - if the model is an encoder, make the mask broadcastable to [batch_size, num_heads, mask_seq_length, mask_seq_length]
             if self.config.is_decoder:
-                seq_ids = torch.arange(seq_length, device=inputs_embeds.device)
-                causal_mask = seq_ids[None, None, :].repeat(batch_size, seq_length, 1) <= seq_ids[None, :, None]
+                seq_ids = torch.arange(mask_seq_length, device=inputs_embeds.device)
+                causal_mask = seq_ids[None, None, :].repeat(batch_size, mask_seq_length, 1) <= seq_ids[None, :, None]
                 causal_mask = causal_mask.to(attention_mask)
                 extended_attention_mask = causal_mask[:, None, :, :] * attention_mask[:, None, None, :]
+                if self.output_past and past_key_value_states[0] is not None:
+                    extended_attention_mask = extended_attention_mask[:, :, -1:, :]
             else:
                 extended_attention_mask = attention_mask[:, None, None, :]
 
@@ -610,9 +717,9 @@ class T5Stack(T5PreTrainedModel):
         extended_attention_mask = extended_attention_mask.to(dtype=next(self.parameters()).dtype)  # fp16 compatibility
         extended_attention_mask = (1.0 - extended_attention_mask) * -1e9
 
-        if self.is_decoder:
+        if self.is_decoder and encoder_attention_mask is not None:
             # If a 2D ou 3D attention mask is provided for the cross-attention
-            # we need to make broadcastabe to [batch_size, num_heads, seq_length, seq_length]
+            # we need to make broadcastabe to [batch_size, num_heads, mask_seq_length, mask_seq_length]
             if encoder_attention_mask.dim() == 3:
                 encoder_extended_attention_mask = encoder_attention_mask[:, None, :, :]
             if encoder_attention_mask.dim() == 2:
@@ -633,7 +740,7 @@ class T5Stack(T5PreTrainedModel):
         # 1.0 in head_mask indicate we keep the head
         # attention_probs has shape bsz x n_heads x N x N
         # input head_mask has shape [num_heads] or [num_hidden_layers x num_heads]
-        # and head_mask is converted to shape [num_hidden_layers x batch x num_heads x seq_length x seq_length]
+        # and head_mask is converted to shape [num_hidden_layers x batch x num_heads x mask_seq_length x mask_seq_length]
         if head_mask is not None:
             if head_mask.dim() == 1:
                 head_mask = head_mask.unsqueeze(0).unsqueeze(0).unsqueeze(-1).unsqueeze(-1)
@@ -648,13 +755,15 @@ class T5Stack(T5PreTrainedModel):
         else:
             head_mask = [None] * self.config.num_layers
 
+        present_key_value_states = ()
         all_hidden_states = ()
         all_attentions = ()
         position_bias = None
         encoder_decoder_position_bias = None
 
         hidden_states = self.dropout(inputs_embeds)
-        for i, layer_module in enumerate(self.block):
+
+        for i, (layer_module, past_key_value_state) in enumerate(zip(self.block, past_key_value_states)):
             if self.output_hidden_states:
                 all_hidden_states = all_hidden_states + (hidden_states,)
 
@@ -666,19 +775,22 @@ class T5Stack(T5PreTrainedModel):
                 encoder_attention_mask=encoder_extended_attention_mask,
                 encoder_decoder_position_bias=encoder_decoder_position_bias,
                 head_mask=head_mask[i],
+                past_key_value_state=past_key_value_state,
             )
             # layer_outputs is a tuple with:
-            # hidden-states, (self-attention weights), (self-attention position bias), (cross-attention weights), (cross-attention position bias)
-            hidden_states = layer_outputs[0]
+            # hidden-states, key-value-states, (self-attention weights), (self-attention position bias), (cross-attention weights), (cross-attention position bias)
+            hidden_states, present_key_value_state = layer_outputs[:2]
             if i == 0:
                 # We share the position biases between the layers - the first layer store them
-                # layer_outputs = hidden-states, (self-attention weights), (self-attention position bias), (cross-attention weights), (cross-attention position bias)
-                position_bias = layer_outputs[2 if self.output_attentions else 1]
+                # layer_outputs = hidden-states, key-value-states (self-attention weights), (self-attention position bias), (cross-attention weights), (cross-attention position bias)
+                position_bias = layer_outputs[3 if self.output_attentions else 2]
                 if self.is_decoder:
-                    encoder_decoder_position_bias = layer_outputs[4 if self.output_attentions else 2]
+                    encoder_decoder_position_bias = layer_outputs[4 if self.output_attentions else 3]
+            # append next layer key value states
+            present_key_value_states = present_key_value_states + (present_key_value_state,)
 
             if self.output_attentions:
-                all_attentions = all_attentions + (layer_outputs[1],)  # We keep only self-attention weights for now
+                all_attentions = all_attentions + (layer_outputs[2],)  # We keep only self-attention weights for now
 
         hidden_states = self.final_layer_norm(hidden_states)
         hidden_states = self.dropout(hidden_states)
@@ -688,11 +800,13 @@ class T5Stack(T5PreTrainedModel):
             all_hidden_states = all_hidden_states + (hidden_states,)
 
         outputs = (hidden_states,)
+        if self.is_decoder and self.output_past:
+            outputs = outputs + (present_key_value_states,)
         if self.output_hidden_states:
             outputs = outputs + (all_hidden_states,)
         if self.output_attentions:
             outputs = outputs + (all_attentions,)
-        return outputs  # last-layer hidden state, (all hidden states), (all attentions)
+        return outputs  # last-layer hidden state, (presents,) (all hidden states), (all attentions)
 
 
 T5_START_DOCSTRING = r"""    The T5 model was proposed in
@@ -719,7 +833,7 @@ T5_INPUTS_DOCSTRING = r"""
     Args:
         input_ids (:obj:`torch.LongTensor` of shape :obj:`(batch_size, sequence_length)`):
             Indices of input sequence tokens in the vocabulary.
-            T5 is a model with relative position embeddings so you should be able to pad the inputs on
+            T5 is a model with relative position embeddings so you should be able to pad the inputs on both the right and the left. If `decoder_past_key_value_states` is used, optionally only the last `input_ids` have to be input (see `decoder_past_key_value_states`).
             Indices can be obtained using :class:`transformers.T5Tokenizer`.
             See :func:`transformers.PreTrainedTokenizer.encode` and
             :func:`transformers.PreTrainedTokenizer.convert_tokens_to_ids` for details.
@@ -739,6 +853,9 @@ T5_INPUTS_DOCSTRING = r"""
             `T5 Training <./t5.html#training>`_ .
         decoder_attention_mask (:obj:`torch.BoolTensor` of shape :obj:`(batch_size, tgt_seq_len)`, `optional`, defaults to :obj:`None`):
             Default behavior: generate a tensor that ignores pad tokens in decoder_input_ids. Causal mask will also be used by default.
+        decoder_past_key_value_states (:obj:`tuple(tuple(torch.FloatTensor))` of length :obj:`config.n_layers` with each tuple having 4 tensors of shape :obj:`(batch_size, num_heads, sequence_length - 1, embed_size_per_head)`):
+            Contains pre-computed key and value hidden-states of the attention blocks.
+            Can be used to speed up decoding. If `decoder_past_key_value_states` are used, the user can optionally input only the last `decoder_input_ids` of shape :obj:`(batch_size, 1)` instead of all `decoder_input_ids` of shape :obj:`(batch_size, sequence_length)`.
         inputs_embeds (:obj:`torch.FloatTensor` of shape :obj:`(batch_size, sequence_length, hidden_size)`, `optional`, defaults to :obj:`None`):
             Optionally, instead of passing :obj:`input_ids` you can choose to directly pass an embedded representation.
             This is useful if you want more control over how to convert `input_ids` indices into associated vectors
@@ -780,6 +897,20 @@ class T5Model(T5PreTrainedModel):
         self.encoder.set_input_embeddings(new_embeddings)
         self.decoder.set_input_embeddings(new_embeddings)
 
+    def set_output_past(self, do_output_past: bool):
+        self.config.output_past = do_output_past
+        self.decoder.output_past = do_output_past
+        for block in self.decoder.block:
+            block.output_past = do_output_past
+            block.layer[0].SelfAttention.output_past = do_output_past
+            block.layer[1].EncDecAttention.output_past = do_output_past
+
+    def get_encoder(self):
+        return self.encoder
+
+    def get_decoder(self):
+        return self.decoder
+
     def _prune_heads(self, heads_to_prune):
         """ Prunes heads of the model.
             heads_to_prune: dict of {layer_num: list of heads to prune in this layer}
@@ -796,6 +927,7 @@ class T5Model(T5PreTrainedModel):
         encoder_outputs=None,
         decoder_input_ids=None,
         decoder_attention_mask=None,
+        decoder_past_key_value_states=None,
         inputs_embeds=None,
         decoder_inputs_embeds=None,
         head_mask=None,
@@ -805,6 +937,11 @@ class T5Model(T5PreTrainedModel):
         :obj:`tuple(torch.FloatTensor)` comprising various elements depending on the configuration (:class:`~transformers.T5Config`) and inputs.
         last_hidden_state (:obj:`torch.FloatTensor` of shape :obj:`(batch_size, sequence_length, hidden_size)`):
             Sequence of hidden-states at the output of the last layer of the model.
+            If `decoder_past_key_value_states` is used only the last hidden-state of the sequences of shape :obj:`(batch_size, 1, hidden_size)` is output.
+        decoder_past_key_value_states (:obj:`tuple(tuple(torch.FloatTensor))` of length :obj:`config.n_layers` with each tuple having 4 tensors of shape :obj:`(batch_size, num_heads, sequence_length, embed_size_per_head)`, `optional`, returned when ``config.output_past=True``):
+            Contains pre-computed key and value hidden-states of the attention blocks.
+            Can be used to speed up sequential decoding (see `decoder_past_key_value_states` input).
+            Note that when using `decoder_past_key_value_states`, the model only outputs the last `hidden-state` of the sequence of shape :obj:`(batch_size, 1, config.vocab_size)`.
         hidden_states (:obj:`tuple(torch.FloatTensor)`, `optional`, returned when ``config.output_hidden_states=True``):
             Tuple of :obj:`torch.FloatTensor` (one for the output of the embeddings + one for the output of each layer)
             of shape :obj:`(batch_size, sequence_length, hidden_size)`.
@@ -837,16 +974,29 @@ class T5Model(T5PreTrainedModel):
 
         hidden_states = encoder_outputs[0]
 
+        # If decoding with past key value states, only the last tokens
+        # should be given as an input
+        if decoder_past_key_value_states is not None and self.decoder.output_past is True:
+            if decoder_input_ids is not None:
+                decoder_input_ids = decoder_input_ids[:, -1:]
+            if decoder_inputs_embeds is not None:
+                decoder_inputs_embeds = decoder_inputs_embeds[:, -1:]
+
         # Decode
         decoder_outputs = self.decoder(
             input_ids=decoder_input_ids,
             attention_mask=decoder_attention_mask,
             inputs_embeds=decoder_inputs_embeds,
+            past_key_value_states=decoder_past_key_value_states,
             encoder_hidden_states=hidden_states,
             encoder_attention_mask=attention_mask,
             head_mask=head_mask,
         )
 
+        if self.decoder.output_past:
+            past = ((encoder_outputs, decoder_outputs[1]),)
+            decoder_outputs = decoder_outputs[:1] + past + decoder_outputs[2:]
+
         return decoder_outputs + encoder_outputs
 
 
@@ -872,6 +1022,14 @@ class T5ForConditionalGeneration(T5PreTrainedModel):
     def get_input_embeddings(self):
         return self.shared
 
+    def set_output_past(self, do_output_past: bool):
+        self.config.output_past = do_output_past
+        self.decoder.output_past = do_output_past
+        for block in self.decoder.block:
+            block.output_past = do_output_past
+            block.layer[0].SelfAttention.output_past = do_output_past
+            block.layer[1].EncDecAttention.output_past = do_output_past
+
     def set_input_embeddings(self, new_embeddings):
         self.shared = new_embeddings
         self.encoder.set_input_embeddings(new_embeddings)
@@ -883,6 +1041,9 @@ class T5ForConditionalGeneration(T5PreTrainedModel):
     def get_encoder(self):
         return self.encoder
 
+    def get_decoder(self):
+        return self.decoder
+
     @add_start_docstrings_to_callable(T5_INPUTS_DOCSTRING)
     def forward(
         self,
@@ -891,6 +1052,7 @@ class T5ForConditionalGeneration(T5PreTrainedModel):
         encoder_outputs=None,
         decoder_input_ids=None,
         decoder_attention_mask=None,
+        decoder_past_key_value_states=None,
         lm_labels=None,
         inputs_embeds=None,
         decoder_inputs_embeds=None,
@@ -909,10 +1071,14 @@ class T5ForConditionalGeneration(T5PreTrainedModel):
             Classification loss (cross entropy).
         prediction_scores (:obj:`torch.FloatTensor` of shape :obj:`(batch_size, sequence_length, config.vocab_size)`)
             Prediction scores of the language modeling head (scores for each vocabulary token before SoftMax).
+            If `past_key_value_states` is used only the last prediction_scores of the sequences of shape :obj:`(batch_size, 1, hidden_size)` is output.
+        decoder_past_key_value_states (:obj:`tuple(tuple(torch.FloatTensor))` of length :obj:`config.n_layers` with each tuple having 4 tensors of shape :obj:`(batch_size, num_heads, sequence_length, embed_size_per_head)`, `optional`, returned when ``config.output_past=True``):
+            Contains pre-computed key and value hidden-states of the attention blocks.
+            Can be used to speed up sequential decoding (see `decoder_past_key_value_states` input).
+            Note that when using `decoder_past_key_value_states`, the model only outputs the last `prediction_score` of the sequence of shape :obj:`(batch_size, 1, config.vocab_size)`.
         hidden_states (:obj:`tuple(torch.FloatTensor)`, `optional`, returned when ``config.output_hidden_states=True``):
             Tuple of :obj:`torch.FloatTensor` (one for the output of the embeddings + one for the output of each layer)
             of shape :obj:`(batch_size, sequence_length, hidden_size)`.
-
             Hidden-states of the model at the output of each layer plus the initial embedding outputs.
         attentions (:obj:`tuple(torch.FloatTensor)`, `optional`, returned when ``config.output_attentions=True``):
             Tuple of :obj:`torch.FloatTensor` (one for each layer) of shape
@@ -948,16 +1114,34 @@ class T5ForConditionalGeneration(T5PreTrainedModel):
             # get decoder inputs from shifting lm labels to the right
             decoder_input_ids = self._shift_right(lm_labels)
 
+        # If decoding with past key value states, only the last tokens
+        # should be given as an input
+        if decoder_past_key_value_states is not None and self.decoder.output_past is True:
+            assert (
+                lm_labels is None
+            ), "Decoder should not use cached key value states when training. Also consider setting model.set_output_past(False) for less memory consumption"
+            if decoder_input_ids is not None:
+                decoder_input_ids = decoder_input_ids[:, -1:]
+            if decoder_inputs_embeds is not None:
+                decoder_inputs_embeds = decoder_inputs_embeds[:, -1:]
+
         # Decode
         decoder_outputs = self.decoder(
             input_ids=decoder_input_ids,
             attention_mask=decoder_attention_mask,
             inputs_embeds=decoder_inputs_embeds,
+            past_key_value_states=decoder_past_key_value_states,
             encoder_hidden_states=hidden_states,
             encoder_attention_mask=attention_mask,
             head_mask=head_mask,
         )
 
+        # insert decoder past at right place
+        # to speed up decoding
+        if self.decoder.output_past:
+            past = ((encoder_outputs, decoder_outputs[1]),)
+            decoder_outputs = decoder_outputs[:1] + past + decoder_outputs[2:]
+
         sequence_output = decoder_outputs[0]
         # Rescale output before projecting on vocab
         # See https://github.com/tensorflow/mesh/blob/fa19d69eafc9a482aff0b59ddd96b025c0cb207d/mesh_tensorflow/transformer/transformer.py#L586
@@ -968,9 +1152,8 @@ class T5ForConditionalGeneration(T5PreTrainedModel):
         if lm_labels is not None:
             loss_fct = CrossEntropyLoss(ignore_index=-100)
             loss = loss_fct(lm_logits.view(-1, lm_logits.size(-1)), lm_labels.view(-1))
-            decoder_outputs = (
-                loss,
-            ) + decoder_outputs  # TODO(thom): Add z_loss https://github.com/tensorflow/mesh/blob/fa19d69eafc9a482aff0b59ddd96b025c0cb207d/mesh_tensorflow/layers.py#L666
+            # TODO(thom): Add z_loss https://github.com/tensorflow/mesh/blob/fa19d69eafc9a482aff0b59ddd96b025c0cb207d/mesh_tensorflow/layers.py#L666
+            decoder_outputs = (loss,) + decoder_outputs
 
         return decoder_outputs + encoder_outputs
 
@@ -978,17 +1161,40 @@ class T5ForConditionalGeneration(T5PreTrainedModel):
         assert past is not None, "past has to be defined for encoder_outputs"
 
         # first step
-        if type(past) is tuple:
-            encoder_outputs = past
+        if len(past) < 2:
+            encoder_outputs, decoder_past_key_value_states = past, None
         else:
-            encoder_outputs = (past,)
+            encoder_outputs, decoder_past_key_value_states = past[0], past[1]
 
         return {
             "decoder_input_ids": input_ids,
+            "decoder_past_key_value_states": decoder_past_key_value_states,
             "encoder_outputs": encoder_outputs,
             "attention_mask": attention_mask,
         }
 
     def _reorder_cache(self, past, beam_idx):
-        # past does not have to be re-ordered for T5.
-        return past
+        # if decoder past is not included in output
+        # speedy decoding is disabled and no need to reorder
+        if len(past) < 2:
+            logger.warning("You might want to consider setting model.set_output_past(True) to speed up decoding")
+            return past
+
+        decoder_past = past[1]
+        past = (past[0],)
+        reordered_decoder_past = ()
+        for layer_past_states in decoder_past:
+            # get the correct batch idx from layer past batch dim
+            # batch dim of `past` is at 2nd position
+            reordered_layer_past_states = ()
+            for layer_past_state in layer_past_states:
+                # need to set correct `past` for each of the four key / value states
+                reordered_layer_past_states = reordered_layer_past_states + (
+                    layer_past_state.index_select(0, beam_idx),
+                )
+
+            assert reordered_layer_past_states[0].shape == layer_past_states[0].shape
+            assert len(reordered_layer_past_states) == len(layer_past_states)
+
+            reordered_decoder_past = reordered_decoder_past + (reordered_layer_past_states,)
+        return past + (reordered_decoder_past,)
diff --git a/src/transformers/modeling_utils.py b/src/transformers/modeling_utils.py
index 685605e773..f52e2b6fa2 100644
--- a/src/transformers/modeling_utils.py
+++ b/src/transformers/modeling_utils.py
@@ -1417,17 +1417,7 @@ class PreTrainedModel(nn.Module, ModuleUtilsMixin):
 
     @staticmethod
     def _reorder_cache(past, beam_idx):
-        reordered_past = []
-        for layer_past in past:
-            # get the correct batch idx from layer past batch dim
-            # batch dim of `past` and `mems` is at 2nd position
-            reordered_layer_past = [layer_past[:, i].unsqueeze(1).clone().detach() for i in beam_idx]
-            reordered_layer_past = torch.cat(reordered_layer_past, dim=1)
-            # check that shape matches
-            assert reordered_layer_past.shape == layer_past.shape
-            reordered_past.append(reordered_layer_past)
-        past = tuple(reordered_past)
-        return past
+        return tuple(layer_past.index_select(1, beam_idx) for layer_past in past)
 
 
 def calc_banned_ngram_tokens(prev_input_ids, num_hypos, no_repeat_ngram_size, cur_len):
diff --git a/tests/test_modeling_common.py b/tests/test_modeling_common.py
index 7ac52a672d..31494a066d 100644
--- a/tests/test_modeling_common.py
+++ b/tests/test_modeling_common.py
@@ -128,6 +128,7 @@ class ModelTesterMixin:
         for model_class in self.all_model_classes:
             config.output_attentions = True
             config.output_hidden_states = False
+            config.output_past = False
             model = model_class(config)
             model.to(torch_device)
             model.eval()
@@ -144,10 +145,9 @@ class ModelTesterMixin:
             out_len = len(outputs)
 
             if self.is_encoder_decoder:
-                correct_outlen = (
-                    4  # decoder_features_or_logits, decoder_attentions, encoder_features, encoder_attentions
-                )
+                correct_outlen = 4
                 decoder_attention_idx = 1
+
                 if "lm_labels" in inputs_dict:  # loss will come first
                     correct_outlen += 1  # compute loss
                     decoder_attention_idx += 1
diff --git a/tests/test_modeling_t5.py b/tests/test_modeling_t5.py
index 1d5e4e9a0a..041ac4a2d9 100644
--- a/tests/test_modeling_t5.py
+++ b/tests/test_modeling_t5.py
@@ -167,17 +167,20 @@ class T5ModelTest(ModelTesterMixin, unittest.TestCase):
             model = T5Model(config=config)
             model.to(torch_device)
             model.eval()
-            decoder_output, encoder_output = model(
+            decoder_output, decoder_past, encoder_output = model(
                 input_ids=input_ids,
                 decoder_input_ids=decoder_input_ids,
                 attention_mask=attention_mask,
                 decoder_attention_mask=decoder_attention_mask,
             )
-            decoder_output, encoder_output = model(input_ids=input_ids, decoder_input_ids=decoder_input_ids)
+            decoder_output, decoder_past, encoder_output = model(
+                input_ids=input_ids, decoder_input_ids=decoder_input_ids
+            )
 
             result = {
                 "encoder_output": encoder_output,
                 "decoder_output": decoder_output,
+                "decoder_past": decoder_past,
             }
             self.parent.assertListEqual(
                 list(result["encoder_output"].size()), [self.batch_size, self.encoder_seq_length, self.hidden_size]
@@ -185,6 +188,13 @@ class T5ModelTest(ModelTesterMixin, unittest.TestCase):
             self.parent.assertListEqual(
                 list(result["decoder_output"].size()), [self.batch_size, self.decoder_seq_length, self.hidden_size]
             )
+            self.parent.assertEqual(len(decoder_past), 2)
+            # decoder_past[0] should correspond to encoder output
+            self.parent.assertTrue(torch.all(decoder_past[0][0] == encoder_output))
+            # There should be `num_layers` key value embeddings stored in decoder_past[1]
+            self.parent.assertEqual(len(decoder_past[1]), config.num_layers)
+            # There should be a self attn key, a self attn value, a cross attn key and a cross attn value stored in each decoder_past[1] tuple
+            self.parent.assertEqual(len(decoder_past[1][0]), 4)
 
         def create_and_check_t5_with_lm_head(
             self, config, input_ids, decoder_input_ids, attention_mask, decoder_attention_mask, lm_labels,
@@ -198,8 +208,8 @@ class T5ModelTest(ModelTesterMixin, unittest.TestCase):
                 decoder_attention_mask=decoder_attention_mask,
                 lm_labels=lm_labels,
             )
-            loss, prediction_scores, encoder_features = outputs
-            self.parent.assertEqual(len(outputs), 3)
+            loss, prediction_scores, _, _ = outputs
+            self.parent.assertEqual(len(outputs), 4)
             result = {
                 "loss": loss,
                 "prediction_scores": prediction_scores,
@@ -209,6 +219,92 @@ class T5ModelTest(ModelTesterMixin, unittest.TestCase):
             )
             self.check_loss_output(result)
 
+        def create_and_check_t5_decoder_model_past(
+            self, config, input_ids, decoder_input_ids, attention_mask, decoder_attention_mask, lm_labels,
+        ):
+            model = T5Model(config=config).get_decoder()
+            model.to(torch_device)
+            model.eval()
+
+            # first forward pass
+            output, past_key_value_states = model(input_ids)
+
+            # create hypothetical next token and extent to next_input_ids
+            next_tokens = ids_tensor((self.batch_size, 1), config.vocab_size)
+
+            # append to next input_ids and
+            next_input_ids = torch.cat([input_ids, next_tokens], dim=-1)
+
+            output_from_no_past, _ = model(next_input_ids)
+            output_from_past, _ = model(next_tokens, past_key_value_states=past_key_value_states)
+
+            # select random slice
+            random_slice_idx = ids_tensor((1,), output_from_past.shape[-1]).item()
+            output_from_no_past_slice = output_from_no_past[:, -1, random_slice_idx].detach()
+            output_from_past_slice = output_from_past[:, 0, random_slice_idx].detach()
+
+            # test that outputs are equal for slice
+            self.parent.assertTrue(torch.allclose(output_from_past_slice, output_from_no_past_slice, atol=1e-3))
+
+        def create_and_check_t5_decoder_model_attention_mask_past(
+            self, config, input_ids, decoder_input_ids, attention_mask, decoder_attention_mask, lm_labels,
+        ):
+            model = T5Model(config=config).get_decoder()
+            model.to(torch_device)
+            model.eval()
+
+            # create attention mask
+            attn_mask = torch.ones(input_ids.shape, dtype=torch.long, device=torch_device)
+
+            half_seq_length = input_ids.shape[-1] // 2
+            attn_mask[:, half_seq_length:] = 0
+
+            # first forward pass
+            output, past_key_value_states = model(input_ids, attention_mask=attn_mask)
+
+            # create hypothetical next token and extent to next_input_ids
+            next_tokens = ids_tensor((self.batch_size, 1), config.vocab_size)
+
+            # change a random masked slice from input_ids
+            random_seq_idx_to_change = ids_tensor((1,), half_seq_length).item() + 1
+            random_other_next_tokens = ids_tensor((self.batch_size, 1), config.vocab_size).squeeze(-1)
+            input_ids[:, -random_seq_idx_to_change] = random_other_next_tokens
+
+            # append to next input_ids and attn_mask
+            next_input_ids = torch.cat([input_ids, next_tokens], dim=-1)
+            attn_mask = torch.cat(
+                [attn_mask, torch.ones((attn_mask.shape[0], 1), dtype=torch.long, device=torch_device)], dim=1,
+            )
+
+            # get two different outputs
+            output_from_no_past, _ = model(next_input_ids, attention_mask=attn_mask)
+            output_from_past, _ = model(
+                next_tokens, past_key_value_states=past_key_value_states, attention_mask=attn_mask
+            )
+
+            # select random slice
+            random_slice_idx = ids_tensor((1,), output_from_past.shape[-1]).item()
+            output_from_no_past_slice = output_from_no_past[:, -1, random_slice_idx].detach()
+            output_from_past_slice = output_from_past[:, 0, random_slice_idx].detach()
+
+            # test that outputs are equal for slice
+            self.parent.assertTrue(torch.allclose(output_from_past_slice, output_from_no_past_slice, atol=1e-3))
+
+        def create_t5_and_check_t5_generate_with_past_key_value_states(
+            self, config, input_ids, decoder_input_ids, attention_mask, decoder_attention_mask, lm_labels,
+        ):
+            config.num_layers = 1
+            model = T5ForConditionalGeneration(config=config)
+            model.to(torch_device)
+            model.eval()
+            torch.manual_seed(0)
+            model.set_output_past(False)
+            output_without_past_cache = model.generate(input_ids[:1], num_beams=2, max_length=5, do_sample=True)
+            torch.manual_seed(0)
+            model.set_output_past(True)
+            output_with_past_cache = model.generate(input_ids[:1], num_beams=2, max_length=5, do_sample=True)
+            self.parent.assertTrue(torch.all(output_with_past_cache == output_without_past_cache))
+
         def prepare_config_and_inputs_for_common(self):
             config_and_inputs = self.prepare_config_and_inputs()
             (
@@ -247,6 +343,18 @@ class T5ModelTest(ModelTesterMixin, unittest.TestCase):
         config_and_inputs = self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_t5_with_lm_head(*config_and_inputs)
 
+    def test_t5_decoder_model_past(self):
+        config_and_inputs = self.model_tester.prepare_config_and_inputs()
+        self.model_tester.create_and_check_t5_decoder_model_past(*config_and_inputs)
+
+    def test_t5_decoder_model_past_with_attn_mask(self):
+        config_and_inputs = self.model_tester.prepare_config_and_inputs()
+        self.model_tester.create_and_check_t5_decoder_model_attention_mask_past(*config_and_inputs)
+
+    def test_t5_generate_with_past_key_value_states(self):
+        config_and_inputs = self.model_tester.prepare_config_and_inputs()
+        self.model_tester.create_t5_and_check_t5_generate_with_past_key_value_states(*config_and_inputs)
+
     @slow
     def test_model_from_pretrained(self):
         for model_name in list(T5_PRETRAINED_MODEL_ARCHIVE_MAP.keys())[:1]: