diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index e1fe2f7fe77e2..e6272b2a97dc1 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -145,7 +145,7 @@ Indexing
 ^^^^^^^^
 
 - Bug in assignment using a reverse slicer (:issue:`26939`)
--
+- Bug in reindexing a :meth:`PeriodIndex` with another type of index that contained a `Period` (:issue:`28323`) (:issue:`28337`)
 
 Missing
 ^^^^^^^
@@ -214,7 +214,7 @@ Other
 - Trying to set the ``display.precision``, ``display.max_rows`` or ``display.max_columns`` using :meth:`set_option` to anything but a ``None`` or a positive int will raise a ``ValueError`` (:issue:`23348`)
 - Using :meth:`DataFrame.replace` with overlapping keys in a nested dictionary will no longer raise, now matching the behavior of a flat dictionary (:issue:`27660`)
 - :meth:`DataFrame.to_csv` and :meth:`Series.to_csv` now support dicts as ``compression`` argument with key ``'method'`` being the compression method and others as additional compression options when the compression method is ``'zip'``. (:issue:`26023`)
-
+-
 
 .. _whatsnew_1000.contributors:
 
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index f7bf77928bdc7..ee85b0fb91acb 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -651,10 +651,13 @@ def get_indexer(self, target, method=None, limit=None, tolerance=None):
 
         if isinstance(target, PeriodIndex):
             target = target.asi8
+            self_index = self._int64index
+        else:
+            self_index = self
 
         if tolerance is not None:
             tolerance = self._convert_tolerance(tolerance, target)
-        return Index.get_indexer(self._int64index, target, method, limit, tolerance)
+        return Index.get_indexer(self_index, target, method, limit, tolerance)
 
     @Appender(_index_shared_docs["get_indexer_non_unique"] % _index_doc_kwargs)
     def get_indexer_non_unique(self, target):
diff --git a/pandas/tests/indexes/period/test_period.py b/pandas/tests/indexes/period/test_period.py
index 8b3b66bd1ee6b..ee37be7ab4c14 100644
--- a/pandas/tests/indexes/period/test_period.py
+++ b/pandas/tests/indexes/period/test_period.py
@@ -354,6 +354,35 @@ def test_period_set_index_reindex(self):
         df = df.set_index(idx2)
         tm.assert_index_equal(df.index, idx2)
 
+    @pytest.mark.parametrize(
+        "p_values, o_values, values, expected_values",
+        [
+            (
+                [Period("2019Q1", "Q-DEC"), Period("2019Q2", "Q-DEC")],
+                [Period("2019Q1", "Q-DEC"), Period("2019Q2", "Q-DEC"), "All"],
+                [1.0, 1.0],
+                [1.0, 1.0, np.nan],
+            ),
+            (
+                [Period("2019Q1", "Q-DEC"), Period("2019Q2", "Q-DEC")],
+                [Period("2019Q1", "Q-DEC"), Period("2019Q2", "Q-DEC")],
+                [1.0, 1.0],
+                [1.0, 1.0],
+            ),
+        ],
+    )
+    def test_period_reindex_with_object(
+        self, p_values, o_values, values, expected_values
+    ):
+        # GH 28337
+        period_index = PeriodIndex(p_values)
+        object_index = Index(o_values)
+
+        s = pd.Series(values, index=period_index)
+        result = s.reindex(object_index)
+        expected = pd.Series(expected_values, index=object_index)
+        tm.assert_series_equal(result, expected)
+
     def test_factorize(self):
         idx1 = PeriodIndex(
             ["2014-01", "2014-01", "2014-02", "2014-02", "2014-03", "2014-03"], freq="M"
diff --git a/pandas/tests/reshape/test_pivot.py b/pandas/tests/reshape/test_pivot.py
index 03b15d2df1a26..582084e3bfb5a 100644
--- a/pandas/tests/reshape/test_pivot.py
+++ b/pandas/tests/reshape/test_pivot.py
@@ -677,6 +677,32 @@ def test_pivot_periods(self, method):
             pv = pd.pivot(df, index="p1", columns="p2", values="data1")
         tm.assert_frame_equal(pv, expected)
 
+    def test_pivot_periods_with_margins(self):
+        # GH 28323
+        df = DataFrame(
+            {
+                "a": [1, 1, 2, 2],
+                "b": [
+                    pd.Period("2019Q1"),
+                    pd.Period("2019Q2"),
+                    pd.Period("2019Q1"),
+                    pd.Period("2019Q2"),
+                ],
+                "x": 1.0,
+            }
+        )
+
+        expected = DataFrame(
+            data=1.0,
+            index=pd.Index([1, 2, "All"], name="a"),
+            columns=pd.Index(
+                [pd.Period("2019Q1"), pd.Period("2019Q2"), "All"], name="b"
+            ),
+        )
+
+        result = df.pivot_table(index="a", columns="b", values="x", margins=True)
+        tm.assert_frame_equal(expected, result)
+
     @pytest.mark.parametrize(
         "values",
         [