diff --git a/doc/source/release.rst b/doc/source/release.rst
index 4b33c20424b33..fde13941d0266 100644
--- a/doc/source/release.rst
+++ b/doc/source/release.rst
@@ -771,6 +771,7 @@ Bug Fixes
   - Fix empty series not printing name in repr (:issue:`4651`)
   - Make tests create temp files in temp directory by default. (:issue:`5419`)
   - ``pd.to_timedelta`` of a scalar returns a scalar (:issue:`5410`)
+  - ``pd.to_timedelta`` accepts ``NaN`` and ``NaT``, returning ``NaT`` instead of raising (:issue:`5437`)
 
 pandas 0.12.0
 -------------
diff --git a/pandas/core/internals.py b/pandas/core/internals.py
index 62aa95d270924..3ce9b9288e8c7 100644
--- a/pandas/core/internals.py
+++ b/pandas/core/internals.py
@@ -1162,15 +1162,25 @@ def _try_fill(self, value):
 
     def _try_coerce_args(self, values, other):
         """ provide coercion to our input arguments
-            we are going to compare vs i8, so coerce to integer
-            values is always ndarra like, other may not be """
-        values = values.view('i8')
+            we are going to compare vs i8, so coerce to floats
+            repring NaT with np.nan so nans propagate
+            values is always ndarray like, other may not be """
+        def masker(v):
+            mask = isnull(v)
+            v = v.view('i8').astype('float64')
+            v[mask] = np.nan
+            return v
+
+        values = masker(values)
+
         if isnull(other) or (np.isscalar(other) and other == tslib.iNaT):
-            other = tslib.iNaT
+            other = np.nan
         elif isinstance(other, np.timedelta64):
             other = _coerce_scalar_to_timedelta_type(other,unit='s').item()
+            if other == tslib.iNaT:
+                other = np.nan
         else:
-            other = other.view('i8')
+            other = masker(other)
 
         return values, other
 
diff --git a/pandas/core/ops.py b/pandas/core/ops.py
index 0c647bb6ee7eb..5e800ffd82306 100644
--- a/pandas/core/ops.py
+++ b/pandas/core/ops.py
@@ -255,7 +255,7 @@ def __init__(self, left, right, name):
         self.name = name
 
         lvalues = self._convert_to_array(left, name=name)
-        rvalues = self._convert_to_array(right, name=name)
+        rvalues = self._convert_to_array(right, name=name, other=lvalues)
 
         self.is_timedelta_lhs = com.is_timedelta64_dtype(left)
         self.is_datetime_lhs = com.is_datetime64_dtype(left)
@@ -317,7 +317,7 @@ def _validate(self):
                             'of a series/ndarray of type datetime64[ns] '
                             'or a timedelta')
 
-    def _convert_to_array(self, values, name=None):
+    def _convert_to_array(self, values, name=None, other=None):
         """converts values to ndarray"""
         from pandas.tseries.timedeltas import _possibly_cast_to_timedelta
 
@@ -325,9 +325,16 @@ def _convert_to_array(self, values, name=None):
         if not is_list_like(values):
             values = np.array([values])
         inferred_type = lib.infer_dtype(values)
+
         if inferred_type in ('datetime64', 'datetime', 'date', 'time'):
+            # if we have a other of timedelta, but use pd.NaT here we
+            # we are in the wrong path
+            if other is not None and other.dtype == 'timedelta64[ns]' and all(isnull(v) for v in values):
+                values = np.empty(values.shape,dtype=other.dtype)
+                values[:] = tslib.iNaT
+
             # a datetlike
-            if not (isinstance(values, (pa.Array, pd.Series)) and
+            elif not (isinstance(values, (pa.Array, pd.Series)) and
                     com.is_datetime64_dtype(values)):
                 values = tslib.array_to_datetime(values)
             elif isinstance(values, pd.DatetimeIndex):
@@ -354,6 +361,15 @@ def _convert_to_array(self, values, name=None):
                                     ', '.join([com.pprint_thing(v)
                                                for v in values[mask]])))
             values = _possibly_cast_to_timedelta(os, coerce=coerce)
+        elif inferred_type == 'floating':
+
+            # all nan, so ok, use the other dtype (e.g. timedelta or datetime)
+            if isnull(values).all():
+                values = np.empty(values.shape,dtype=other.dtype)
+                values[:] = tslib.iNaT
+            else:
+                raise TypeError("incompatible type [{0}] for a datetime/timedelta"
+                                " operation".format(pa.array(values).dtype))
         else:
             raise TypeError("incompatible type [{0}] for a datetime/timedelta"
                             " operation".format(pa.array(values).dtype))
@@ -452,6 +468,8 @@ def na_op(x, y):
 
     def wrapper(left, right, name=name):
 
+        if isinstance(right, pd.DataFrame):
+            return NotImplemented
         time_converted = _TimeOp.maybe_convert_for_time_op(left, right, name)
 
         if time_converted is None:
@@ -488,8 +506,6 @@ def wrapper(left, right, name=name):
 
             return left._constructor(wrap_results(arr), index=index,
                                      name=name, dtype=dtype)
-        elif isinstance(right, pd.DataFrame):
-            return NotImplemented
         else:
             # scalars
             if hasattr(lvalues, 'values'):
diff --git a/pandas/tseries/tests/test_timedeltas.py b/pandas/tseries/tests/test_timedeltas.py
index 199ad19986b39..df03851ca4ddb 100644
--- a/pandas/tseries/tests/test_timedeltas.py
+++ b/pandas/tseries/tests/test_timedeltas.py
@@ -195,6 +195,122 @@ def test_timedelta_ops(self):
         expected = to_timedelta('00:00:08')
         tm.assert_almost_equal(result, expected)
 
+    def test_to_timedelta_on_missing_values(self):
+        _skip_if_numpy_not_friendly()
+
+        # GH5438
+        timedelta_NaT = np.timedelta64('NaT')
+
+        actual = pd.to_timedelta(Series(['00:00:01', np.nan]))
+        expected = Series([np.timedelta64(1000000000, 'ns'), timedelta_NaT], dtype='<m8[ns]')
+        assert_series_equal(actual, expected)
+
+        actual = pd.to_timedelta(Series(['00:00:01', pd.NaT]))
+        assert_series_equal(actual, expected)
+
+        actual = pd.to_timedelta(np.nan)
+        self.assert_(actual == timedelta_NaT)
+
+        actual = pd.to_timedelta(pd.NaT)
+        self.assert_(actual == timedelta_NaT)
+
+    def test_timedelta_ops_with_missing_values(self):
+        _skip_if_numpy_not_friendly()
+
+        # setup
+        s1 = pd.to_timedelta(Series(['00:00:01']))
+        s2 = pd.to_timedelta(Series(['00:00:02']))
+        sn = pd.to_timedelta(Series([pd.NaT]))
+        df1 = DataFrame(['00:00:01']).apply(pd.to_timedelta)
+        df2 = DataFrame(['00:00:02']).apply(pd.to_timedelta)
+        dfn = DataFrame([pd.NaT]).apply(pd.to_timedelta)
+        scalar1 = pd.to_timedelta('00:00:01')
+        scalar2 = pd.to_timedelta('00:00:02')
+        timedelta_NaT = pd.to_timedelta('NaT')
+        NA = np.nan
+
+        actual = scalar1 + scalar1
+        self.assert_(actual == scalar2)
+        actual = scalar2 - scalar1
+        self.assert_(actual == scalar1)
+
+        actual = s1 + s1
+        assert_series_equal(actual, s2)
+        actual = s2 - s1
+        assert_series_equal(actual, s1)
+
+        actual = s1 + scalar1
+        assert_series_equal(actual, s2)
+        actual = s2 - scalar1
+        assert_series_equal(actual, s1)
+
+        actual = s1 + timedelta_NaT
+        assert_series_equal(actual, sn)
+        actual = s1 - timedelta_NaT
+        assert_series_equal(actual, sn)
+
+        actual = s1 + NA
+        assert_series_equal(actual, sn)
+        actual = s1 - NA
+        assert_series_equal(actual, sn)
+
+        actual = s1 + pd.NaT  # NaT is datetime, not timedelta
+        assert_series_equal(actual, sn)
+        actual = s2 - pd.NaT
+        assert_series_equal(actual, sn)
+
+        actual = s1 + df1
+        assert_frame_equal(actual, df2)
+        actual = s2 - df1
+        assert_frame_equal(actual, df1)
+        actual = df1 + s1
+        assert_frame_equal(actual, df2)
+        actual = df2 - s1
+        assert_frame_equal(actual, df1)
+
+        actual = df1 + df1
+        assert_frame_equal(actual, df2)
+        actual = df2 - df1
+        assert_frame_equal(actual, df1)
+
+        actual = df1 + scalar1
+        assert_frame_equal(actual, df2)
+        actual = df2 - scalar1
+        assert_frame_equal(actual, df1)
+
+        actual = df1 + timedelta_NaT
+        assert_frame_equal(actual, dfn)
+        actual = df1 - timedelta_NaT
+        assert_frame_equal(actual, dfn)
+
+        actual = df1 + NA
+        assert_frame_equal(actual, dfn)
+        actual = df1 - NA
+        assert_frame_equal(actual, dfn)
+
+        actual = df1 + pd.NaT  # NaT is datetime, not timedelta
+        assert_frame_equal(actual, dfn)
+        actual = df1 - pd.NaT
+        assert_frame_equal(actual, dfn)
+
+    def test_apply_to_timedelta(self):
+        _skip_if_numpy_not_friendly()
+
+        timedelta_NaT = pd.to_timedelta('NaT')
+
+        list_of_valid_strings = ['00:00:01', '00:00:02']
+        a = pd.to_timedelta(list_of_valid_strings)
+        b = Series(list_of_valid_strings).apply(pd.to_timedelta)
+        # Can't compare until apply on a Series gives the correct dtype
+        # assert_series_equal(a, b)
+
+        list_of_strings = ['00:00:01', np.nan, pd.NaT, timedelta_NaT]
+        a = pd.to_timedelta(list_of_strings)
+        b = Series(list_of_strings).apply(pd.to_timedelta)
+        # Can't compare until apply on a Series gives the correct dtype
+        # assert_series_equal(a, b)
+
+
 if __name__ == '__main__':
     nose.runmodule(argv=[__file__, '-vvs', '-x', '--pdb', '--pdb-failure'],
                    exit=False)
diff --git a/pandas/tseries/timedeltas.py b/pandas/tseries/timedeltas.py
index 862dc8d410996..835401a13403f 100644
--- a/pandas/tseries/timedeltas.py
+++ b/pandas/tseries/timedeltas.py
@@ -9,7 +9,7 @@
 import pandas.tslib as tslib
 from pandas import compat, _np_version_under1p7
 from pandas.core.common import (ABCSeries, is_integer, is_timedelta64_dtype,
-                                _values_from_object, is_list_like)
+                                _values_from_object, is_list_like, isnull)
 
 repr_timedelta = tslib.repr_timedelta64
 repr_timedelta64 = tslib.repr_timedelta64
@@ -84,6 +84,8 @@ def conv(v):
         r = conv(r)
     elif r == tslib.iNaT:
         return r
+    elif isnull(r):
+        return np.timedelta64('NaT')
     elif isinstance(r, np.timedelta64):
         r = r.astype("m8[{0}]".format(unit.lower()))
     elif is_integer(r):