diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index 9840e4e94d28c..9aa374f92a9aa 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -206,8 +206,8 @@ Groupby/resample/rolling
 Reshaping
 ^^^^^^^^^
 
+- Bug in :meth:`DataFrame.apply` that caused incorrect output with empty :class:`DataFrame` (:issue:`28202`, :issue:`21959`)
 - Bug in :meth:`DataFrame.stack` not handling non-unique indexes correctly when creating MultiIndex (:issue: `28301`)
--
 
 Sparse
 ^^^^^^
diff --git a/pandas/core/apply.py b/pandas/core/apply.py
index e6766a33a613b..61d093d19e4be 100644
--- a/pandas/core/apply.py
+++ b/pandas/core/apply.py
@@ -204,17 +204,20 @@ def apply_empty_result(self):
         from pandas import Series
 
         if not should_reduce:
-
-            EMPTY_SERIES = Series([])
             try:
-                r = self.f(EMPTY_SERIES, *self.args, **self.kwds)
+                r = self.f(Series([]))
             except Exception:
                 pass
             else:
                 should_reduce = not isinstance(r, Series)
 
         if should_reduce:
-            return self.obj._constructor_sliced(np.nan, index=self.agg_axis)
+            if len(self.agg_axis):
+                r = self.f(Series([]))
+            else:
+                r = np.nan
+
+            return self.obj._constructor_sliced(r, index=self.agg_axis)
         else:
             return self.obj.copy()
 
diff --git a/pandas/tests/frame/test_apply.py b/pandas/tests/frame/test_apply.py
index 92912ff9ec093..0328232213588 100644
--- a/pandas/tests/frame/test_apply.py
+++ b/pandas/tests/frame/test_apply.py
@@ -116,6 +116,27 @@ def test_apply_with_reduce_empty(self):
         # Ensure that x.append hasn't been called
         assert x == []
 
+    @pytest.mark.parametrize("func", ["sum", "prod", "any", "all"])
+    def test_apply_funcs_over_empty(self, func):
+        # GH 28213
+        df = DataFrame(columns=["a", "b", "c"])
+
+        result = df.apply(getattr(np, func))
+        expected = getattr(df, func)()
+        assert_series_equal(result, expected)
+
+    def test_nunique_empty(self):
+        # GH 28213
+        df = DataFrame(columns=["a", "b", "c"])
+
+        result = df.nunique()
+        expected = Series(0, index=df.columns)
+        assert_series_equal(result, expected)
+
+        result = df.T.nunique()
+        expected = Series([], index=pd.Index([]))
+        assert_series_equal(result, expected)
+
     def test_apply_deprecate_reduce(self):
         empty_frame = DataFrame()