diff --git a/CHANGELOG.md b/CHANGELOG.md
index ee67fbe..0ffa566 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -18,6 +18,11 @@ and this project adheres to [Semantic Versioning][].
 
 - `update()`, `push_obs()`, `push_var()`, `pull_obs()`, and `pull_var()` now try harder to preserve the dtype of the dataframe columns
 
+### Deprecated
+
+- `MuData.mod_names`, `MuData.obs_keys`, `MuData.var_keys`, `MuData.obsm_keys`, `MuData.varm_keys`, `MuData.uns_keys`, `MuData.obs_vector`, `MuData.var_vector`.
+  Their analogs in AnnData will be deprecated in AnnData 0.13.
+
 ## [0.3.3]
 
 ### Fixed
diff --git a/pyproject.toml b/pyproject.toml
index 673c277..0c6f694 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -34,7 +34,7 @@ dependencies = [
   "numpy",
   "pandas>=1.4",
   "scipy",
-  "scverse-misc",
+  "scverse-misc>=0.0.3",
   # for debug logging (referenced from the issue template)
   "session-info2",
 ]
diff --git a/src/mudata/_core/mudata.py b/src/mudata/_core/mudata.py
index a1edf1d..61aa398 100644
--- a/src/mudata/_core/mudata.py
+++ b/src/mudata/_core/mudata.py
@@ -20,6 +20,7 @@
 from anndata._core.aligned_mapping import AxisArraysBase
 from anndata._core.views import DataFrameView
 from anndata.utils import convert_to_dict
+from scverse_misc import Deprecation, deprecated
 
 from .compat import AlignedView, AxisArrays, PairwiseArrays
 from .config import OPTIONS
@@ -1248,6 +1249,7 @@ def _attr_vector(self, key: str, attr: str) -> np.ndarray:
             raise KeyError(f"There is no key {key} in MuData .{attr} or in .{attr} of any modalities.")
         return df[key].to_numpy()
 
+    @deprecated(Deprecation("0.3.4"))
     def obs_vector(self, key: str, layer: str | None = None) -> np.ndarray:
         """Return an array of values for the requested key of length n_obs.
 
@@ -1391,6 +1393,7 @@ def n_var(self) -> int:
         # )
         return self._var.shape[0]
 
+    @deprecated(Deprecation("0.3.4"))
     def var_vector(self, key: str, layer: str | None = None) -> np.ndarray:
         """Return an array of values for the requested key of length n_var.
 
@@ -1558,22 +1561,27 @@ def uns(self):
     # _keys methods to increase compatibility
     # with calls requiring those AnnData methods
 
+    @deprecated(Deprecation("0.3.4", msg="Use `obs.columns` instead."))
     def obs_keys(self) -> list[str]:
         """List keys of observation annotation :attr:`obs`."""
         return self._obs.keys().tolist()
 
+    @deprecated(Deprecation("0.3.4", msg="Use `var.columns` instead."))
     def var_keys(self) -> list[str]:
         """List keys of variable annotation :attr:`var`."""
         return self._var.keys().tolist()
 
+    @deprecated(Deprecation("0.3.4", msg="Use `obsm.keys()` instead."))
     def obsm_keys(self) -> list[str]:
         """List keys of observation annotation :attr:`obsm`."""
         return list(self._obsm.keys())
 
+    @deprecated(Deprecation("0.3.4", msg="Use `varm.keys()` instead."))
     def varm_keys(self) -> list[str]:
         """List keys of variable annotation :attr:`varm`."""
         return list(self._varm.keys())
 
+    @deprecated(Deprecation("0.3.4", msg="Use `uns.keys()` instead."))
     def uns_keys(self) -> list[str]:
         """List keys of unstructured annotation."""
         return list(self._uns.keys())
@@ -1599,6 +1607,7 @@ def axis(self) -> Literal[-1, 0, 1]:
         return self._axis
 
     @property
+    @deprecated(Deprecation("0.3.4", msg="Use `mod.keys()` instead."))
     def mod_names(self) -> list[str]:
         """Names of modalities (alias for `list(mdata.mod.keys())`)"""
         return list(self._mod.keys())
diff --git a/src/mudata/_core/utils.py b/src/mudata/_core/utils.py
index f4ef8cf..29df25d 100644
--- a/src/mudata/_core/utils.py
+++ b/src/mudata/_core/utils.py
@@ -1,12 +1,14 @@
+from __future__ import annotations
+
 from collections import Counter
-from collections.abc import Mapping, Sequence
 from contextlib import suppress
-from typing import Literal, TypeVar
+from typing import TYPE_CHECKING, Literal
 
 import numpy as np
 import pandas as pd
 
-T = TypeVar("T", pd.Series, pd.DataFrame)
+if TYPE_CHECKING:
+    from collections.abc import Mapping, Sequence
 
 
 def _make_index_unique(df: pd.DataFrame, force: bool = False) -> pd.DataFrame: