diff --git a/doc/source/api.rst b/doc/source/api.rst
index fff944651588e..9faac4c616477 100644
--- a/doc/source/api.rst
+++ b/doc/source/api.rst
@@ -444,6 +444,7 @@ Reindexing / Selection / Label manipulation
 
    Series.align
    Series.drop
+   Series.droplevel
    Series.drop_duplicates
    Series.duplicated
    Series.equals
@@ -1063,6 +1064,7 @@ Reshaping, sorting, transposing
 .. autosummary::
    :toctree: generated/
 
+   DataFrame.droplevel
    DataFrame.pivot
    DataFrame.pivot_table
    DataFrame.reorder_levels
diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 034a56b2ac0cb..d300c2b273906 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -74,6 +74,7 @@ Other Enhancements
 - :func:`Series.mode` and :func:`DataFrame.mode` now support the ``dropna`` parameter which can be used to specify whether NaN/NaT values should be considered (:issue:`17534`)
 - :func:`to_csv` now supports ``compression`` keyword when a file handle is passed. (:issue:`21227`)
 - :meth:`Index.droplevel` is now implemented also for flat indexes, for compatibility with :class:`MultiIndex` (:issue:`21115`)
+- :meth:`Series.droplevel` and :meth:`DataFrame.droplevel` are now implemented (:issue:`20342`)
 - Added support for reading from Google Cloud Storage via the ``gcsfs`` library (:issue:`19454`)
 - :func:`to_gbq` and :func:`read_gbq` signature and documentation updated to
   reflect changes from the `Pandas-GBQ library version 0.5.0
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 8da678e0adec0..608eebd079eef 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -716,6 +716,66 @@ def swapaxes(self, axis1, axis2, copy=True):
 
         return self._constructor(new_values, *new_axes).__finalize__(self)
 
+    def droplevel(self, level, axis=0):
+        """Return DataFrame with requested index / column level(s) removed.
+
+        .. versionadded:: 0.24.0
+
+        Parameters
+        ----------
+        level : int, str, or list-like
+            If a string is given, must be the name of a level
+            If list-like, elements must be names or positional indexes
+            of levels.
+
+        axis : {0 or 'index', 1 or 'columns'}, default 0
+
+
+        Returns
+        -------
+        DataFrame.droplevel()
+
+        Examples
+        --------
+        >>> df = pd.DataFrame([
+        ...:     [1, 2, 3, 4],
+        ...:     [5, 6, 7, 8],
+        ...:     [9, 10, 11, 12]
+        ...: ]).set_index([0, 1]).rename_axis(['a', 'b'])
+
+        >>> df.columns = pd.MultiIndex.from_tuples([
+        ...:    ('c', 'e'), ('d', 'f')
+        ...:], names=['level_1', 'level_2'])
+
+        >>> df
+        level_1   c   d
+        level_2   e   f
+        a b
+        1 2      3   4
+        5 6      7   8
+        9 10    11  12
+
+        >>> df.droplevel('a')
+        level_1   c   d
+        level_2   e   f
+        b
+        2        3   4
+        6        7   8
+        10      11  12
+
+        >>> df.droplevel('level2', axis=1)
+        level_1   c   d
+        a b
+        1 2      3   4
+        5 6      7   8
+        9 10    11  12
+
+        """
+        labels = self._get_axis(axis)
+        new_labels = labels.droplevel(level)
+        result = self.set_axis(new_labels, axis=axis, inplace=False)
+        return result
+
     def pop(self, item):
         """
         Return item and drop from frame. Raise KeyError if not found.
diff --git a/pandas/tests/frame/test_alter_axes.py b/pandas/tests/frame/test_alter_axes.py
index 21961906c39bb..4f95eb3fe7b47 100644
--- a/pandas/tests/frame/test_alter_axes.py
+++ b/pandas/tests/frame/test_alter_axes.py
@@ -1056,6 +1056,28 @@ def test_reindex_signature(self):
                               "limit", "copy", "level", "method",
                               "fill_value", "tolerance"}
 
+    def test_droplevel(self):
+        # GH20342
+        df = pd.DataFrame([
+            [1, 2, 3, 4],
+            [5, 6, 7, 8],
+            [9, 10, 11, 12]
+        ])
+        df = df.set_index([0, 1]).rename_axis(['a', 'b'])
+        df.columns = pd.MultiIndex.from_tuples([('c', 'e'), ('d', 'f')],
+                                               names=['level_1', 'level_2'])
+
+        # test that dropping of a level in index works
+        expected = df.reset_index('a', drop=True)
+        result = df.droplevel('a', axis='index')
+        assert_frame_equal(result, expected)
+
+        # test that dropping of a level in columns works
+        expected = df.copy()
+        expected.columns = pd.Index(['c', 'd'], name='level_1')
+        result = df.droplevel('level_2', axis='columns')
+        assert_frame_equal(result, expected)
+
 
 class TestIntervalIndex(object):
 
diff --git a/pandas/tests/series/test_alter_axes.py b/pandas/tests/series/test_alter_axes.py
index 859082a7e722d..840c80d6775a5 100644
--- a/pandas/tests/series/test_alter_axes.py
+++ b/pandas/tests/series/test_alter_axes.py
@@ -295,3 +295,15 @@ def test_reset_index_drop_errors(self):
         s = pd.Series(range(4), index=pd.MultiIndex.from_product([[1, 2]] * 2))
         with tm.assert_raises_regex(KeyError, 'not found'):
             s.reset_index('wrong', drop=True)
+
+    def test_droplevel(self):
+        # GH20342
+        ser = pd.Series([1, 2, 3, 4])
+        ser.index = pd.MultiIndex.from_arrays([(1, 2, 3, 4), (5, 6, 7, 8)],
+                                              names=['a', 'b'])
+        expected = ser.reset_index('b', drop=True)
+        result = ser.droplevel('b', axis='index')
+        assert_series_equal(result, expected)
+        # test that droplevel raises ValueError on axis != 0
+        with pytest.raises(ValueError):
+            ser.droplevel(1, axis='columns')