diff --git a/pandas/core/indexes/accessors.py b/pandas/core/indexes/accessors.py
index ce3143b342cec..02729ff90d51a 100644
--- a/pandas/core/indexes/accessors.py
+++ b/pandas/core/indexes/accessors.py
@@ -11,6 +11,7 @@
     is_timedelta64_dtype, is_categorical_dtype,
     is_list_like)
 
+
 from pandas.core.base import PandasDelegate, NoNewAttributesMixin
 from pandas.core.indexes.datetimes import DatetimeIndex
 from pandas._libs.period import IncompatibleFrequency  # noqa
@@ -48,8 +49,10 @@ def maybe_to_datetimelike(data, copy=False):
     DelegatedClass
 
     """
-    from pandas import Series
+    from pandas import Series, Index
 
+    if isinstance(data, Index):
+        data = data.to_series()
     if not isinstance(data, Series):
         raise TypeError("cannot convert an object of type {0} to a "
                         "datetimelike index".format(type(data)))
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 4aecc75d95971..e5ac7cf601369 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -1592,6 +1592,13 @@ def is_all_dates(self):
             return False
         return is_datetime_array(_ensure_object(self.values))
 
+    @property
+    def dt(self):
+        # Non-raising versions of the `.dt` attribute are available in
+        # DatetimeIndex, PeriodIndex, and TimedeltaIndex.
+        raise AttributeError("Can only use .dt accessor with datetimelike "
+                             "values")
+
     def __iter__(self):
         return iter(self.values)
 
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 845c71b6c41d8..09602408fa2bb 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -125,6 +125,21 @@ def ceil(self, freq):
 class DatetimeIndexOpsMixin(object):
     """ common ops mixin to support a unified inteface datetimelike Index """
 
+    @cache_readonly
+    def dt(self):
+        """
+        For a datetime-like Index object, `self.dt` returns `self` so that
+        datetime-like attributes can be accessed symmetrically for Index
+        and Series objects.
+
+        For Index objects that are not datetime-like, `self.dt` will raise
+        and AttributeError.
+        """
+        # Note: we use a `cache_readonly` instead of AccessorProperty
+        # to avoid circular imports.
+        from pandas.core.indexes import accessors
+        return accessors.CombinedDatetimelikeProperties._make_accessor(self)
+
     def equals(self, other):
         """
         Determines if two Index objects contain the same elements.
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index ef36e4a91aa1c..4c46c83b76b74 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -1444,6 +1444,47 @@ def test_join_self(self):
                 joined = res.join(res, how=kind)
                 assert res is joined
 
+    def test_dt_accessor(self):
+        # index.dt should raise AttributeError for all index classes other
+        # than DatetimeIndex, PeriodIndex, and TimedeltaIndex
+        no_dt_examples = [pd.Index([np.nan]),
+                          pd.Index([np.nan, 1]),
+                          pd.Index([1, 2, np.nan]),
+                          pd.Index(['foo', 'bar']),
+                          pd.RangeIndex(12),
+                          pd.CategoricalIndex(['a', 'b', np.nan])]
+
+        dr = pd.date_range('1994-10-06', periods=4, freq='D')
+        mi = pd.MultiIndex.from_product([[1, 2], ['foo', 'bar'], dr])
+        no_dt_examples.append(mi)
+        mi2 = pd.MultiIndex.from_product([range(3), dr])
+        no_dt_examples.append(mi2)
+
+        for index in no_dt_examples:
+            # Note: in py2, `hasattr` will return False when attempting
+            # to access the attribute raises.
+            assert not hasattr(index, 'dt')
+
+        dt_examples = [dr,
+                       pd.to_datetime(['NaT']),
+                       pd.to_datetime(['NaT', '2000-01-01']),
+                       pd.to_datetime(['2000-01-01', 'NaT', '2000-01-02']),
+                       pd.to_timedelta(['1 day', 'NaT'])
+                       ]
+
+        for index in dt_examples:
+            assert hasattr(index, 'dt')
+            # Note: index.dt.day returns a Series that has index as its
+            # index, whereas index.day is just a index containing the day
+            # values.
+            dt = index.dt
+            if isinstance(index, pd.TimedeltaIndex):
+                tm.assert_almost_equal(dt.days.values, index.days.values)
+                tm.assert_almost_equal(dt.seconds.values, index.seconds.values)
+            else:
+                tm.assert_almost_equal(dt.day.values, index.day.values)
+                tm.assert_almost_equal(dt.year.values, index.year.values)
+
     def test_str_attribute(self):
         # GH9068
         methods = ['strip', 'rstrip', 'lstrip']