diff --git a/pyproject.toml b/pyproject.toml
index 309e5d3..55b04b7 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -48,7 +48,7 @@ dev = [
   "pre-commit",
   "twine>=4.0.2",
 ]
-test = [ "coverage>=7.10", "mudata[io]", "pytest" ]
+test = [ "coverage>=7.10", "mudata[io]", "packaging", "pytest" ]
 doc = [
   "docutils>=0.8,!=0.18.*,!=0.19.*",
   "ipykernel",
diff --git a/src/mudata/_core/mudata.py b/src/mudata/_core/mudata.py
index 9e9e54a..123ab95 100644
--- a/src/mudata/_core/mudata.py
+++ b/src/mudata/_core/mudata.py
@@ -533,9 +533,28 @@ def strings_to_categoricals(self, df: pd.DataFrame | None = None) -> pd.DataFram
     def __getitem__(self, index) -> AnnData | MuData:
         if isinstance(index, str):
             return self._mod[index]
+        elif type(index).__module__.startswith("anndata.acc") and type(index).__name__ == "AdRef":
+            try:
+                return index.acc.get(self, index.idx)
+            except KeyError as e:
+                if index.acc.dim in ("obs", "var"):
+                    for modname, mod in self._mod.items():
+                        if index in mod:
+                            raise KeyError(
+                                f"There is no key {index.idx} in MuData .{index.acc.dim} but there is one in {modname} .{index.acc.dim}. Consider running `pull_{index.acc.dim}()` to update global .{index.acc.dim}."
+                            ) from e
+                raise
         else:
             return MuData(self, as_view=True, index=index)
 
+    def __contains__(self, key) -> bool:
+        if isinstance(key, str):
+            return key in self._mod
+        elif type(key).__module__.startswith("anndata.acc") and type(key).__name__ == "AdRef":
+            return AnnData.__contains__.__get__(self)(key)
+        else:
+            raise TypeError(f"Unexpected key {key!r}.")
+
     @property
     def mod(self) -> Mapping[str, AnnData | MuData]:
         """Dictionary of modalities."""
diff --git a/tests/test_obs_var.py b/tests/test_obs_var.py
index 3057c50..4636b4f 100644
--- a/tests/test_obs_var.py
+++ b/tests/test_obs_var.py
@@ -1,8 +1,10 @@
 from pathlib import Path
 
+import anndata as ad
 import numpy as np
 import pandas as pd
 import pytest
+from packaging.version import Version
 
 import mudata as md
 
@@ -145,3 +147,15 @@ def test_names_make_unique(mdata: md.MuData):
 
     with pytest.raises(TypeError, match="axis="):
         getattr(mdata, f"{attr}_names_make_unique")()
+
+
+@pytest.mark.skipif(
+    Version(ad.__version__) < Version("0.13dev0"), reason="anndata version too old, no accessor support"
+)
+def test_accessors(mdata: md.MuData):
+    assert ad.acc.A.obs["arange"] in mdata
+    assert (mdata[ad.acc.A.obs["arange"]] == mdata.obs["arange"]).all()
+    with pytest.raises(KeyError, match="test"):
+        mdata[ad.acc.A.var["test"]]
+    with pytest.raises(KeyError, match="there is one in"):
+        mdata[ad.acc.A.var["assert-bool"]]
diff --git a/tests/test_update.py b/tests/test_update.py
index 0a32eb0..318ff49 100644
--- a/tests/test_update.py
+++ b/tests/test_update.py
@@ -146,6 +146,9 @@ def test_update_simple(mdata: MuData, axis: Axis):
     for mod in mdata.mod.keys():
         assert mdata.obsmap[mod].dtype.kind == "u"
         assert mdata.varmap[mod].dtype.kind == "u"
+        assert mod in mdata
+    with pytest.raises(TypeError):
+        1 in mdata  # noqa: B015
 
     # names along non-axis are concatenated
     assert mdata.shape[1 - axis] == sum(mod.shape[1 - axis] for mod in mdata.mod.values())