diff --git a/pymc/sampling/mcmc.py b/pymc/sampling/mcmc.py
index 4b26bb51c8..fec0d7c145 100644
--- a/pymc/sampling/mcmc.py
+++ b/pymc/sampling/mcmc.py
@@ -246,7 +246,7 @@ def _print_step_hierarchy(s: Step, level: int = 0) -> None:
     else:
         varnames = ", ".join(
             [
-                get_untransformed_name(v.name) if is_transformed_name(v.name) else v.name
+                get_untransformed_name(v.name) if is_transformed_name(v.name) else v.name  # type: ignore[arg-type, misc]
                 for v in s.vars
             ]
         )
diff --git a/pymc/util.py b/pymc/util.py
index 6d4b1bf4de..42835915f6 100644
--- a/pymc/util.py
+++ b/pymc/util.py
@@ -14,9 +14,9 @@
 
 import warnings
 
-from collections.abc import Sequence
+from collections.abc import Callable, Iterable, Sequence
 from copy import deepcopy
-from typing import NewType, cast
+from typing import Any, NewType, TypeVar, cast
 
 import arviz
 import cloudpickle
@@ -32,8 +32,10 @@
 
 from pymc.exceptions import BlockModelAccessError
 
+T = TypeVar("T")
 
-def __getattr__(name):
+
+def __getattr__(name: str) -> Callable:
     if name == "dataset_to_point_list":
         warnings.warn(
             f"{name} has been moved to backends.arviz. Importing from util will fail in a future release.",
@@ -160,8 +162,8 @@ def tree_contains(self, item):
             return dict.__contains__(self, item)
 
 
-def get_transformed_name(name, transform):
-    r"""
+def get_transformed_name(name: str, transform) -> str:
+    """
     Consistent way of transforming names.
 
     Parameters
@@ -179,8 +181,8 @@ def get_transformed_name(name, transform):
     return f"{name}_{transform.name}__"
 
 
-def is_transformed_name(name):
-    r"""
+def is_transformed_name(name: str) -> bool:
+    """
     Quickly check if a name was transformed with `get_transformed_name`.
 
     Parameters
@@ -196,8 +198,8 @@ def is_transformed_name(name):
     return name.endswith("__") and name.count("_") >= 3
 
 
-def get_untransformed_name(name):
-    r"""
+def get_untransformed_name(name: str) -> str:
+    """
     Undo transformation in `get_transformed_name`. Throws ValueError if name wasn't transformed.
 
     Parameters
@@ -215,8 +217,13 @@ def get_untransformed_name(name):
     return "_".join(name.split("_")[:-3])
 
 
-def get_default_varnames(var_iterator, include_transformed):
-    r"""Extract default varnames from a trace.
+VarOrVarName = TypeVar("VarOrVarName", Variable, str)
+
+
+def get_default_varnames(
+    var_iterator: Iterable[VarOrVarName], include_transformed: bool
+) -> list[VarOrVarName]:
+    """Extract default varnames from a trace.
 
     Parameters
     ----------
@@ -236,7 +243,7 @@ def get_default_varnames(var_iterator, include_transformed):
         return [var for var in var_iterator if not is_transformed_name(get_var_name(var))]
 
 
-def get_var_name(var) -> VarName:
+def get_var_name(var: VarOrVarName) -> VarName:
     """Get an appropriate, plain variable name for a variable."""
     return VarName(str(getattr(var, "name", var)))
 
@@ -280,7 +287,7 @@ def chains_and_samples(data: xarray.Dataset | arviz.InferenceData) -> tuple[int,
     return nchains, nsamples
 
 
-def hashable(a=None) -> int:
+def hashable(a: Any = None) -> int:
     """
     Hash many kinds of objects, including some that are unhashable through the builtin `hash` function.
 
@@ -516,8 +523,8 @@ def _add_future_warning_tag(var) -> None:
         var.tag = new_tag
 
 
-def makeiter(a):
-    if isinstance(a, tuple | list):
+def makeiter(a: Sequence[T] | T) -> Sequence[T]:
+    if isinstance(a, Sequence):
         return a
     else:
         return [a]