diff --git a/pandas-stubs/core/indexes/interval.pyi b/pandas-stubs/core/indexes/interval.pyi
index c1474174b..aeef461fe 100644
--- a/pandas-stubs/core/indexes/interval.pyi
+++ b/pandas-stubs/core/indexes/interval.pyi
@@ -371,7 +371,7 @@ def interval_range(
     start: _TimestampLike,
     end: _TimestampLike = ...,
     periods: int | None = ...,
-    freq: str | BaseOffset | None = ...,
+    freq: str | BaseOffset | pd.Timedelta | dt.timedelta | None = ...,
     name: Hashable = ...,
     closed: IntervalClosedType = ...,
 ) -> IntervalIndex[Interval[pd.Timestamp]]: ...
@@ -381,7 +381,7 @@ def interval_range(
     start: None = ...,
     end: _TimestampLike,
     periods: int | None = ...,
-    freq: str | BaseOffset | None = ...,
+    freq: str | BaseOffset | pd.Timedelta | dt.timedelta | None = ...,
     name: Hashable = ...,
     closed: IntervalClosedType = ...,
 ) -> IntervalIndex[Interval[pd.Timestamp]]: ...
@@ -391,7 +391,7 @@ def interval_range(
     *,
     end: None = ...,
     periods: int | None = ...,
-    freq: str | BaseOffset | None = ...,
+    freq: str | BaseOffset | pd.Timedelta | dt.timedelta | None = ...,
     name: Hashable = ...,
     closed: IntervalClosedType = ...,
 ) -> IntervalIndex[Interval[pd.Timestamp]]: ...
@@ -400,7 +400,7 @@ def interval_range(
     start: _TimedeltaLike,
     end: _TimedeltaLike = ...,
     periods: int | None = ...,
-    freq: str | BaseOffset | None = ...,
+    freq: str | BaseOffset | pd.Timedelta | dt.timedelta | None = ...,
     name: Hashable = ...,
     closed: IntervalClosedType = ...,
 ) -> IntervalIndex[Interval[pd.Timedelta]]: ...
@@ -410,7 +410,7 @@ def interval_range(
     start: None = ...,
     end: _TimedeltaLike,
     periods: int | None = ...,
-    freq: str | BaseOffset | None = ...,
+    freq: str | BaseOffset | pd.Timedelta | dt.timedelta | None = ...,
     name: Hashable = ...,
     closed: IntervalClosedType = ...,
 ) -> IntervalIndex[Interval[pd.Timedelta]]: ...
@@ -420,7 +420,7 @@ def interval_range(
     *,
     end: None = ...,
     periods: int | None = ...,
-    freq: str | BaseOffset | None = ...,
+    freq: str | BaseOffset | pd.Timedelta | dt.timedelta | None = ...,
     name: Hashable = ...,
     closed: IntervalClosedType = ...,
 ) -> IntervalIndex[Interval[pd.Timedelta]]: ...
diff --git a/pandas-stubs/core/indexes/timedeltas.pyi b/pandas-stubs/core/indexes/timedeltas.pyi
index 545898190..9a58bdc0d 100644
--- a/pandas-stubs/core/indexes/timedeltas.pyi
+++ b/pandas-stubs/core/indexes/timedeltas.pyi
@@ -72,7 +72,7 @@ def timedelta_range(
     start: TimedeltaConvertibleTypes = ...,
     end: TimedeltaConvertibleTypes = ...,
     periods: int | None = ...,
-    freq: str | DateOffset | None = ...,
+    freq: str | DateOffset | Timedelta | dt.timedelta | None = ...,
     name: Hashable | None = ...,
     closed: Literal["left", "right"] | None = ...,
 ) -> TimedeltaIndex: ...
diff --git a/pandas-stubs/core/series.pyi b/pandas-stubs/core/series.pyi
index c53c288bb..41c1e9f27 100644
--- a/pandas-stubs/core/series.pyi
+++ b/pandas-stubs/core/series.pyi
@@ -179,7 +179,13 @@ class _LocIndexerSeries(_LocIndexer, Generic[S1]):
     @overload
     def __getitem__(
         self,
-        idx: MaskType | Index | Sequence[float] | list[str] | slice | _IndexSliceTuple,
+        idx: MaskType
+        | Index
+        | Sequence[float]
+        | list[str]
+        | slice
+        | _IndexSliceTuple
+        | Callable,
         # _IndexSliceTuple is when having a tuple that includes a slice.  Could just
         # be s.loc[1, :], or s.loc[pd.IndexSlice[1, :]]
     ) -> Series[S1]: ...
@@ -775,7 +781,7 @@ class Series(IndexOpsMixin, NDFrame, Generic[S1]):
     @overload
     def apply(
         self,
-        func: Callable[..., Scalar | Sequence | set | Mapping],
+        func: Callable[..., Scalar | Sequence | set | Mapping | None],
         convertDType: _bool = ...,
         args: tuple = ...,
         **kwds,
diff --git a/tests/test_indexes.py b/tests/test_indexes.py
index 2c337a35d..fa4557600 100644
--- a/tests/test_indexes.py
+++ b/tests/test_indexes.py
@@ -291,6 +291,30 @@ def test_interval_range():
         pd.IntervalIndex,
         pd.Interval,
     )
+    check(
+        assert_type(
+            pd.interval_range(
+                pd.Timestamp(2000, 1, 1),
+                pd.Timestamp(2010, 1, 1),
+                freq=pd.Timedelta(days=30),
+            ),
+            "pd.IntervalIndex[pd.Interval[pd.Timestamp]]",
+        ),
+        pd.IntervalIndex,
+        pd.Interval,
+    )
+    check(
+        assert_type(
+            pd.interval_range(
+                pd.Timestamp(2000, 1, 1),
+                pd.Timestamp(2010, 1, 1),
+                freq=dt.timedelta(days=30),
+            ),
+            "pd.IntervalIndex[pd.Interval[pd.Timestamp]]",
+        ),
+        pd.IntervalIndex,
+        pd.Interval,
+    )
     check(
         assert_type(
             pd.interval_range(pd.Timestamp(2000, 1, 1), dt.datetime(2010, 1, 1), 5),
@@ -308,6 +332,26 @@ def test_interval_range():
         pd.IntervalIndex,
         pd.Interval,
     )
+    check(
+        assert_type(
+            pd.interval_range(
+                pd.Timedelta("1D"), pd.Timedelta("10D"), freq=pd.Timedelta("2D")
+            ),
+            "pd.IntervalIndex[pd.Interval[pd.Timedelta]]",
+        ),
+        pd.IntervalIndex,
+        pd.Interval,
+    )
+    check(
+        assert_type(
+            pd.interval_range(
+                pd.Timedelta("1D"), pd.Timedelta("10D"), freq=dt.timedelta(days=2)
+            ),
+            "pd.IntervalIndex[pd.Interval[pd.Timedelta]]",
+        ),
+        pd.IntervalIndex,
+        pd.Interval,
+    )
     check(
         assert_type(
             pd.interval_range(end=pd.Timedelta("10D"), periods=10, freq="D"),
diff --git a/tests/test_series.py b/tests/test_series.py
index d37d0726a..f76c2662d 100644
--- a/tests/test_series.py
+++ b/tests/test_series.py
@@ -1820,3 +1820,15 @@ def test_convert_dtypes_dtype_backend() -> None:
     s = pd.Series([1, 2, 3, 4])
     s1 = s.convert_dtypes(dtype_backend="numpy_nullable")
     check(assert_type(s1, pd.Series), pd.Series)
+
+
+def test_apply_returns_none() -> None:
+    # GH 557
+    s = pd.Series([1, 2, 3])
+    check(assert_type(s.apply(lambda x: None), pd.Series), pd.Series)
+
+
+def test_loc_callable() -> None:
+    # GH 586
+    s = pd.Series([1, 2])
+    check(assert_type(s.loc[lambda x: x > 1], pd.Series), pd.Series)
diff --git a/tests/test_timefuncs.py b/tests/test_timefuncs.py
index fe5c80677..e1d6e329c 100644
--- a/tests/test_timefuncs.py
+++ b/tests/test_timefuncs.py
@@ -1071,6 +1071,20 @@ def test_timedelta_range() -> None:
         ),
         pd.TimedeltaIndex,
     )
+    check(
+        assert_type(
+            pd.timedelta_range("1 day", "10 days", freq=pd.Timedelta("2 days")),
+            pd.TimedeltaIndex,
+        ),
+        pd.TimedeltaIndex,
+    )
+    check(
+        assert_type(
+            pd.timedelta_range("1 day", "10 days", freq=dt.timedelta(days=2)),
+            pd.TimedeltaIndex,
+        ),
+        pd.TimedeltaIndex,
+    )
 
 
 def test_dateoffset_freqstr() -> None: