diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index d8dc8ae68c347..f83aa0ce87d3b 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -217,6 +217,8 @@ Categorical
 
 - Added test to assert the :func:`fillna` raises the correct ValueError message when the value isn't a value from categories (:issue:`13628`)
 - Bug in :meth:`Categorical.astype` where ``NaN`` values were handled incorrectly when casting to int (:issue:`28406`)
+- Bug in :meth:`Categorical.astype` not allowing for casting to extension dtypes (:issue:`28668`)
+- Bug where :func:`merge` was unable to join on categorical and extension dtype columns (:issue:`28668`)
 - :meth:`Categorical.searchsorted` and :meth:`CategoricalIndex.searchsorted` now work on unordered categoricals also (:issue:`21667`)
 - Added test to assert roundtripping to parquet with :func:`DataFrame.to_parquet` or :func:`read_parquet` will preserve Categorical dtypes for string types (:issue:`27955`)
 -
diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index 33d1de01fa3db..b7431033dae59 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -57,7 +57,7 @@
 )
 from pandas.core.base import NoNewAttributesMixin, PandasObject, _shared_docs
 import pandas.core.common as com
-from pandas.core.construction import extract_array, sanitize_array
+from pandas.core.construction import array, extract_array, sanitize_array
 from pandas.core.missing import interpolate_2d
 from pandas.core.sorting import nargsort
 
@@ -520,6 +520,8 @@ def astype(self, dtype: Dtype, copy: bool = True) -> ArrayLike:
             if dtype == self.dtype:
                 return self
             return self._set_dtype(dtype)
+        if is_extension_array_dtype(dtype):
+            return array(self, dtype=dtype, copy=copy)  # type: ignore # GH 28770
         if is_integer_dtype(dtype) and self.isna().any():
             msg = "Cannot convert float NaN to integer"
             raise ValueError(msg)
diff --git a/pandas/tests/extension/test_categorical.py b/pandas/tests/extension/test_categorical.py
index c342777b0ebc4..e70e4f2fe501b 100644
--- a/pandas/tests/extension/test_categorical.py
+++ b/pandas/tests/extension/test_categorical.py
@@ -207,6 +207,22 @@ def test_cast_nan_to_int(self, cls, values):
         with pytest.raises((ValueError, TypeError), match=msg):
             s.astype(int)
 
+    @pytest.mark.parametrize(
+        "expected",
+        [
+            pd.Series(["2019", "2020"], dtype="datetime64[ns, UTC]"),
+            pd.Series([0, 0], dtype="timedelta64[ns]"),
+            pd.Series([pd.Period("2019"), pd.Period("2020")], dtype="period[A-DEC]"),
+            pd.Series([pd.Interval(0, 1), pd.Interval(1, 2)], dtype="interval"),
+            pd.Series([1, np.nan], dtype="Int64"),
+        ],
+    )
+    def test_cast_category_to_extension_dtype(self, expected):
+        # GH 28668
+        result = expected.astype("category").astype(expected.dtype)
+
+        tm.assert_series_equal(result, expected)
+
 
 class TestArithmeticOps(base.BaseArithmeticOpsTests):
     def test_arith_series_with_scalar(self, data, all_arithmetic_operators):
diff --git a/pandas/tests/reshape/merge/test_merge.py b/pandas/tests/reshape/merge/test_merge.py
index 63de9777756cc..4de8bba169438 100644
--- a/pandas/tests/reshape/merge/test_merge.py
+++ b/pandas/tests/reshape/merge/test_merge.py
@@ -2096,6 +2096,20 @@ def test_merge_equal_cat_dtypes2():
     tm.assert_frame_equal(result, expected, check_categorical=False)
 
 
+def test_merge_on_cat_and_ext_array():
+    # GH 28668
+    right = DataFrame(
+        {"a": Series([pd.Interval(0, 1), pd.Interval(1, 2)], dtype="interval")}
+    )
+    left = right.copy()
+    left["a"] = left["a"].astype("category")
+
+    result = pd.merge(left, right, how="inner", on="a")
+    expected = right.copy()
+
+    assert_frame_equal(result, expected)
+
+
 def test_merge_multiindex_columns():
     # Issue #28518
     # Verify that merging two dataframes give the expected labels