diff --git a/docs/source/reference/data.rst b/docs/source/reference/data.rst
index 852592992b9..607be49211a 100644
--- a/docs/source/reference/data.rst
+++ b/docs/source/reference/data.rst
@@ -148,6 +148,7 @@ using the following components:
     LazyMemmapStorage
     LazyTensorStorage
     ListStorage
+    LazyStackStorage
     ListStorageCheckpointer
     NestedStorageCheckpointer
     PrioritizedSampler
diff --git a/test/test_rb.py b/test/test_rb.py
index a139d34f1a5..b63f888453d 100644
--- a/test/test_rb.py
+++ b/test/test_rb.py
@@ -81,6 +81,7 @@
 
 from torchrl.data.replay_buffers.storages import (
     LazyMemmapStorage,
+    LazyStackStorage,
     LazyTensorStorage,
     ListStorage,
     StorageEnsemble,
@@ -1116,6 +1117,31 @@ def test_storage_inplace_writing_ndim(self, storage_type):
         assert (rb[:, 10:20] == 0).all()
         assert len(rb) == 100
 
+    @pytest.mark.parametrize("max_size", [1000, None])
+    @pytest.mark.parametrize("stack_dim", [-1, 0])
+    def test_lazy_stack_storage(self, max_size, stack_dim):
+        # Create an instance of LazyStackStorage with given parameters
+        storage = LazyStackStorage(max_size=max_size, stack_dim=stack_dim)
+        # Create a ReplayBuffer using the created storage
+        rb = ReplayBuffer(storage=storage)
+        # Generate some random data to add to the buffer
+        torch.manual_seed(0)
+        data0 = TensorDict(a=torch.randn((10,)), b=torch.rand(4), c="a string!")
+        data1 = TensorDict(a=torch.randn((11,)), b=torch.rand(4), c="another string!")
+        # Add the data to the buffer
+        rb.add(data0)
+        rb.add(data1)
+        # Sample from the buffer
+        sample = rb.sample(10)
+        # Check that the sampled data has the correct shape and type
+        assert isinstance(sample, LazyStackedTensorDict)
+        assert sample["b"].shape[0] == 10
+        assert all(isinstance(item, str) for item in sample["c"])
+        # If densify is True, check that the sampled data is dense
+        sample = sample.densify(layout=torch.jagged)
+        assert isinstance(sample["a"], torch.Tensor)
+        assert sample["a"].shape[0] == 10
+
 
 @pytest.mark.parametrize("max_size", [1000])
 @pytest.mark.parametrize("shape", [[3, 4]])
diff --git a/torchrl/data/__init__.py b/torchrl/data/__init__.py
index 3ed65d59d16..7fa882cbbaa 100644
--- a/torchrl/data/__init__.py
+++ b/torchrl/data/__init__.py
@@ -23,6 +23,7 @@
     H5StorageCheckpointer,
     ImmutableDatasetWriter,
     LazyMemmapStorage,
+    LazyStackStorage,
     LazyTensorStorage,
     ListStorage,
     ListStorageCheckpointer,
diff --git a/torchrl/data/replay_buffers/__init__.py b/torchrl/data/replay_buffers/__init__.py
index 25822dcfe4c..4f230f30701 100644
--- a/torchrl/data/replay_buffers/__init__.py
+++ b/torchrl/data/replay_buffers/__init__.py
@@ -32,6 +32,7 @@
 )
 from .storages import (
     LazyMemmapStorage,
+    LazyStackStorage,
     LazyTensorStorage,
     ListStorage,
     Storage,
diff --git a/torchrl/data/replay_buffers/samplers.py b/torchrl/data/replay_buffers/samplers.py
index fc27401d5e5..fa92d84295a 100644
--- a/torchrl/data/replay_buffers/samplers.py
+++ b/torchrl/data/replay_buffers/samplers.py
@@ -1049,6 +1049,10 @@ def __init__(
             self._cache["stop-and-length"] = vals
 
         else:
+            if traj_key is not None:
+                self._fetch_traj = True
+            elif end_key is not None:
+                self._fetch_traj = False
             if end_key is None:
                 end_key = ("next", "done")
             if traj_key is None:
@@ -1331,7 +1335,7 @@ def sample(self, storage: Storage, batch_size: int) -> Tuple[torch.Tensor, dict]
         if start_idx.shape[1] != storage.ndim:
             raise RuntimeError(
                 f"Expected the end-of-trajectory signal to be "
-                f"{storage.ndim}-dimensional. Got a {start_idx.shape[1]} tensor "
+                f"{storage.ndim}-dimensional. Got a tensor with shape[1]={start_idx.shape[1]} "
                 "instead."
             )
         seq_length, num_slices = self._adjusted_batch_size(batch_size)
diff --git a/torchrl/data/replay_buffers/storages.py b/torchrl/data/replay_buffers/storages.py
index 52d137208ad..344814e728c 100644
--- a/torchrl/data/replay_buffers/storages.py
+++ b/torchrl/data/replay_buffers/storages.py
@@ -297,7 +297,15 @@ def set(
     def get(self, index: Union[int, Sequence[int], slice]) -> Any:
         if isinstance(index, (INT_CLASSES, slice)):
             return self._storage[index]
+        elif isinstance(index, tuple):
+            if len(index) > 1:
+                raise RuntimeError(
+                    f"{type(self).__name__} can only be indexed with one-length tuples."
+                )
+            return self.get(index[0])
         else:
+            if isinstance(index, torch.Tensor) and index.device.type != "cpu":
+                index = index.cpu().tolist()
             return [self._storage[i] for i in index]
 
     def __len__(self):
@@ -353,6 +361,77 @@ def contains(self, item):
         raise NotImplementedError(f"type {type(item)} is not supported yet.")
 
 
+class LazyStackStorage(ListStorage):
+    """A ListStorage that returns LazyStackTensorDict instances.
+
+    This storage allows for heterougeneous structures to be indexed as a single `TensorDict` representation.
+    It uses :class:`~tensordict.LazyStackedTensorDict` which operates on non-contiguous lists of tensordicts,
+    lazily stacking items when queried.
+    This means that this storage is going to be fast to sample but data access may be slow (as it requires a stack).
+    Tensors of heterogeneous shapes can also be stored within the storage and stacked together.
+    Because the storage is represented as a list, the number of tensors to store in memory will grow linearly with
+    the size of the buffer.
+
+    If possible, nested tensors can also be created via :meth:`~tensordict.LazyStackedTensorDict.densify`
+    (see :mod:`~torch.nested`).
+
+    Args:
+        max_size (int, optional): the maximum number of elements stored in the storage.
+            If not provided, an unlimited storage is created.
+
+    Keyword Args:
+        compilable (bool, optional): if ``True``, the storage will be made compatible with :func:`~torch.compile` at
+            the cost of being executable in multiprocessed settings.
+        stack_dim (int, optional): the stack dimension in terms of TensorDict batch sizes. Defaults to `-1`.
+
+    Examples:
+        >>> import torch
+        >>> from torchrl.data import ReplayBuffer, LazyStackStorage
+        >>> from tensordict import TensorDict
+        >>> _ = torch.manual_seed(0)
+        >>> rb = ReplayBuffer(storage=LazyStackStorage(max_size=1000, stack_dim=-1))
+        >>> data0 = TensorDict(a=torch.randn((10,)), b=torch.rand(4), c="a string!")
+        >>> data1 = TensorDict(a=torch.randn((11,)), b=torch.rand(4), c="another string!")
+        >>> _ = rb.add(data0)
+        >>> _ = rb.add(data1)
+        >>> rb.sample(10)
+        LazyStackedTensorDict(
+            fields={
+                a: Tensor(shape=torch.Size([10, -1]), device=cpu, dtype=torch.float32, is_shared=False),
+                b: Tensor(shape=torch.Size([10, 4]), device=cpu, dtype=torch.float32, is_shared=False),
+                c: NonTensorStack(
+                    ['another string!', 'another string!', 'another st...,
+                    batch_size=torch.Size([10]),
+                    device=None)},
+            exclusive_fields={
+            },
+            batch_size=torch.Size([10]),
+            device=None,
+            is_shared=False,
+            stack_dim=0)
+    """
+
+    def __init__(
+        self,
+        max_size: int | None = None,
+        *,
+        compilable: bool = False,
+        stack_dim: int = -1,
+    ):
+        super().__init__(max_size=max_size, compilable=compilable)
+        self.stack_dim = stack_dim
+
+    def get(self, index: Union[int, Sequence[int], slice]) -> Any:
+        out = super().get(index=index)
+        if isinstance(out, list):
+            stack_dim = self.stack_dim
+            if stack_dim < 0:
+                stack_dim = out[0].ndim + 1 + stack_dim
+            out = LazyStackedTensorDict(*out, stack_dim=stack_dim)
+            return out
+        return out
+
+
 class TensorStorage(Storage):
     """A storage for tensors and tensordicts.