diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index c01b04991e52b..6b2ed2199703d 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -14,7 +14,7 @@
 import pandas.compat as compat
 from pandas.errors import (
     AbstractMethodError, NullFrequencyError, PerformanceWarning)
-from pandas.util._decorators import Appender, deprecate_kwarg
+from pandas.util._decorators import Appender, Substitution, deprecate_kwarg
 
 from pandas.core.dtypes.common import (
     is_bool_dtype, is_datetime64_any_dtype, is_datetime64_dtype,
@@ -86,44 +86,45 @@ class DatelikeOps(object):
     Common ops for DatetimeIndex/PeriodIndex, but not TimedeltaIndex.
     """
 
+    @Substitution(URL="https://docs.python.org/3/library/datetime.html"
+                      "#strftime-and-strptime-behavior")
     def strftime(self, date_format):
-        from pandas import Index
-        return Index(self.format(date_format=date_format),
-                     dtype=compat.text_type)
-    strftime.__doc__ = """
-    Convert to Index using specified date_format.
+        """
+        Convert to Index using specified date_format.
 
-    Return an Index of formatted strings specified by date_format, which
-    supports the same string format as the python standard library. Details
-    of the string format can be found in `python string format doc <{0}>`__
+        Return an Index of formatted strings specified by date_format, which
+        supports the same string format as the python standard library. Details
+        of the string format can be found in `python string format
+        doc <%(URL)s>`__
 
-    Parameters
-    ----------
-    date_format : str
-        Date format string (e.g. "%Y-%m-%d").
+        Parameters
+        ----------
+        date_format : str
+            Date format string (e.g. "%%Y-%%m-%%d").
 
-    Returns
-    -------
-    Index
-        Index of formatted strings
-
-    See Also
-    --------
-    to_datetime : Convert the given argument to datetime.
-    DatetimeIndex.normalize : Return DatetimeIndex with times to midnight.
-    DatetimeIndex.round : Round the DatetimeIndex to the specified freq.
-    DatetimeIndex.floor : Floor the DatetimeIndex to the specified freq.
-
-    Examples
-    --------
-    >>> rng = pd.date_range(pd.Timestamp("2018-03-10 09:00"),
-    ...                     periods=3, freq='s')
-    >>> rng.strftime('%B %d, %Y, %r')
-    Index(['March 10, 2018, 09:00:00 AM', 'March 10, 2018, 09:00:01 AM',
-           'March 10, 2018, 09:00:02 AM'],
-          dtype='object')
-    """.format("https://docs.python.org/3/library/datetime.html"
-               "#strftime-and-strptime-behavior")
+        Returns
+        -------
+        Index
+            Index of formatted strings
+
+        See Also
+        --------
+        to_datetime : Convert the given argument to datetime.
+        DatetimeIndex.normalize : Return DatetimeIndex with times to midnight.
+        DatetimeIndex.round : Round the DatetimeIndex to the specified freq.
+        DatetimeIndex.floor : Floor the DatetimeIndex to the specified freq.
+
+        Examples
+        --------
+        >>> rng = pd.date_range(pd.Timestamp("2018-03-10 09:00"),
+        ...                     periods=3, freq='s')
+        >>> rng.strftime('%%B %%d, %%Y, %%r')
+        Index(['March 10, 2018, 09:00:00 AM', 'March 10, 2018, 09:00:01 AM',
+               'March 10, 2018, 09:00:02 AM'],
+              dtype='object')
+        """
+        from pandas import Index
+        return Index(self._format_native_types(date_format=date_format))
 
 
 class TimelikeOps(object):
@@ -298,6 +299,23 @@ def asi8(self):
         # do not cache or you'll create a memory leak
         return self._data.view('i8')
 
+    # ----------------------------------------------------------------
+    # Rendering Methods
+
+    def _format_native_types(self, na_rep=u'NaT', date_format=None):
+        """
+        Helper method for astype when converting to strings.
+
+        Returns
+        -------
+        ndarray[str]
+        """
+        raise AbstractMethodError(self)
+
+    def _formatter(self, boxed=False):
+        # TODO: Remove Datetime & DatetimeTZ formatters.
+        return "'{}'".format
+
     # ----------------------------------------------------------------
     # Array-Like / EA-Interface Methods
 
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index c197d6d6e634b..59e9fe49f650a 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -468,6 +468,18 @@ def _validate_fill_value(self, fill_value):
                              "Got '{got}'.".format(got=fill_value))
         return fill_value
 
+    # -----------------------------------------------------------------
+    # Rendering Methods
+
+    def _format_native_types(self, na_rep=u'NaT', date_format=None, **kwargs):
+        from pandas.io.formats.format import _get_format_datetime64_from_values
+        fmt = _get_format_datetime64_from_values(self, date_format)
+
+        return tslib.format_array_from_datetime(self.asi8,
+                                                tz=self.tz,
+                                                format=fmt,
+                                                na_rep=na_rep)
+
     # -----------------------------------------------------------------
     # Comparison Methods
 
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index 60febc5f5636d..6fd98bb25380a 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -92,7 +92,9 @@ def wrapper(self, other):
     return compat.set_function_name(wrapper, opname, cls)
 
 
-class PeriodArray(dtl.DatetimeLikeArrayMixin, ExtensionArray):
+class PeriodArray(dtl.DatetimeLikeArrayMixin,
+                  dtl.DatelikeOps,
+                  ExtensionArray):
     """
     Pandas ExtensionArray for storing Period data.
 
@@ -565,7 +567,7 @@ def asfreq(self, freq=None, how='E'):
         return type(self)(new_data, freq=freq)
 
     # ------------------------------------------------------------------
-    # Formatting
+    # Rendering Methods
 
     def _format_native_types(self, na_rep=u'NaT', date_format=None, **kwargs):
         """
@@ -589,9 +591,7 @@ def _format_native_types(self, na_rep=u'NaT', date_format=None, **kwargs):
             values = np.array([formatter(dt) for dt in values])
         return values
 
-    # Delegation...
-    def strftime(self, date_format):
-        return self._format_native_types(date_format=date_format)
+    # ------------------------------------------------------------------
 
     def repeat(self, repeats, *args, **kwargs):
         """
diff --git a/pandas/core/arrays/timedeltas.py b/pandas/core/arrays/timedeltas.py
index a5d074df338ee..314a3948f1032 100644
--- a/pandas/core/arrays/timedeltas.py
+++ b/pandas/core/arrays/timedeltas.py
@@ -231,6 +231,16 @@ def _validate_fill_value(self, fill_value):
                              "Got '{got}'.".format(got=fill_value))
         return fill_value
 
+    # ----------------------------------------------------------------
+    # Rendering Methods
+
+    def _formatter(self, boxed=False):
+        from pandas.io.formats.format import _get_format_timedelta64
+        return _get_format_timedelta64(self, box=True)
+
+    def _format_native_types(self):
+        return self.astype(object)
+
     # ----------------------------------------------------------------
     # Arithmetic Methods