diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 109005364fca6..81b7aa07b4c0b 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -603,6 +603,8 @@ Datetimelike
 - Bug when comparing a :class:`PeriodIndex` against a zero-dimensional numpy array (:issue:`26689`)
 - Bug in constructing a ``Series`` or ``DataFrame`` from a numpy ``datetime64`` array with a non-ns unit and out-of-bound timestamps generating rubbish data, which will now correctly raise an ``OutOfBoundsDatetime`` error (:issue:`26206`).
 - Bug in :func:`date_range` with unnecessary ``OverflowError`` being raised for very large or very small dates (:issue:`26651`)
+- Bug where adding :class:`Timestamp` to a ``np.timedelta64`` object would raise instead of returning a :class:`Timestamp` (:issue:`24775`)
+- Bug where comparing a zero-dimensional numpy array containing a ``np.datetime64`` object to a :class:`Timestamp` would incorrect raise ``TypeError`` (:issue:`26916`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/_libs/tslibs/c_timestamp.pyx b/pandas/_libs/tslibs/c_timestamp.pyx
index 6bf6b6dcea8dd..f9d1a906207fe 100644
--- a/pandas/_libs/tslibs/c_timestamp.pyx
+++ b/pandas/_libs/tslibs/c_timestamp.pyx
@@ -55,6 +55,9 @@ def maybe_integer_op_deprecated(obj):
 
 cdef class _Timestamp(datetime):
 
+    # higher than np.ndarray and np.matrix
+    __array_priority__ = 100
+
     def __hash__(_Timestamp self):
         if self.nanosecond:
             return hash(self.value)
@@ -85,6 +88,15 @@ cdef class _Timestamp(datetime):
                 if ndim == 0:
                     if is_datetime64_object(other):
                         other = self.__class__(other)
+                    elif is_array(other):
+                        # zero-dim array, occurs if try comparison with
+                        #  datetime64 scalar on the left hand side
+                        # Unfortunately, for datetime64 values, other.item()
+                        #  incorrectly returns an integer, so we need to use
+                        #  the numpy C api to extract it.
+                        other = cnp.PyArray_ToScalar(cnp.PyArray_DATA(other),
+                                                     other)
+                        other = self.__class__(other)
                     else:
                         return NotImplemented
                 elif is_array(other):
diff --git a/pandas/tests/scalar/timestamp/test_arithmetic.py b/pandas/tests/scalar/timestamp/test_arithmetic.py
index 21e1dccaefc4b..8310b140b50e0 100644
--- a/pandas/tests/scalar/timestamp/test_arithmetic.py
+++ b/pandas/tests/scalar/timestamp/test_arithmetic.py
@@ -112,3 +112,23 @@ def test_addition_subtraction_preserve_frequency(self):
         td64 = np.timedelta64(1, 'D')
         assert (ts + td64).freq == original_freq
         assert (ts - td64).freq == original_freq
+
+    @pytest.mark.parametrize('td', [Timedelta(hours=3),
+                                    np.timedelta64(3, 'h'),
+                                    timedelta(hours=3)])
+    def test_radd_tdscalar(self, td):
+        # GH#24775 timedelta64+Timestamp should not raise
+        ts = Timestamp.now()
+        assert td + ts == ts + td
+
+    @pytest.mark.parametrize('other,expected_difference', [
+        (np.timedelta64(-123, 'ns'), -123),
+        (np.timedelta64(1234567898, 'ns'), 1234567898),
+        (np.timedelta64(-123, 'us'), -123000),
+        (np.timedelta64(-123, 'ms'), -123000000)
+    ])
+    def test_timestamp_add_timedelta64_unit(self, other, expected_difference):
+        ts = Timestamp(datetime.utcnow())
+        result = ts + other
+        valdiff = result.value - ts.value
+        assert valdiff == expected_difference
diff --git a/pandas/tests/scalar/timestamp/test_comparisons.py b/pandas/tests/scalar/timestamp/test_comparisons.py
index 763cfc23ea832..b572b4607108c 100644
--- a/pandas/tests/scalar/timestamp/test_comparisons.py
+++ b/pandas/tests/scalar/timestamp/test_comparisons.py
@@ -156,6 +156,18 @@ def test_timestamp_compare_with_early_datetime(self):
         assert stamp < datetime(2700, 1, 1)
         assert stamp <= datetime(2700, 1, 1)
 
+    def test_compare_zerodim_array(self):
+        # GH#26916
+        ts = Timestamp.now()
+        dt64 = np.datetime64('2016-01-01', 'ns')
+        arr = np.array(dt64)
+        assert arr.ndim == 0
+
+        result = arr < ts
+        assert result is True
+        result = arr > ts
+        assert result is False
+
 
 def test_rich_comparison_with_unsupported_type():
     # Comparisons with unsupported objects should return NotImplemented
diff --git a/pandas/tests/scalar/timestamp/test_timestamp.py b/pandas/tests/scalar/timestamp/test_timestamp.py
index 4b6b0dac916c6..b9946796a4e1f 100644
--- a/pandas/tests/scalar/timestamp/test_timestamp.py
+++ b/pandas/tests/scalar/timestamp/test_timestamp.py
@@ -796,31 +796,6 @@ def test_tz_conversion_freq(self, tz_naive_fixture):
 
 class TestTimestampNsOperations:
 
-    def setup_method(self, method):
-        self.timestamp = Timestamp(datetime.utcnow())
-
-    def assert_ns_timedelta(self, modified_timestamp, expected_value):
-        value = self.timestamp.value
-        modified_value = modified_timestamp.value
-
-        assert modified_value - value == expected_value
-
-    def test_timedelta_ns_arithmetic(self):
-        self.assert_ns_timedelta(self.timestamp + np.timedelta64(-123, 'ns'),
-                                 -123)
-
-    def test_timedelta_ns_based_arithmetic(self):
-        self.assert_ns_timedelta(self.timestamp + np.timedelta64(
-            1234567898, 'ns'), 1234567898)
-
-    def test_timedelta_us_arithmetic(self):
-        self.assert_ns_timedelta(self.timestamp + np.timedelta64(-123, 'us'),
-                                 -123000)
-
-    def test_timedelta_ms_arithmetic(self):
-        time = self.timestamp + np.timedelta64(-123, 'ms')
-        self.assert_ns_timedelta(time, -123000000)
-
     def test_nanosecond_string_parsing(self):
         ts = Timestamp('2013-05-01 07:15:45.123456789')
         # GH 7878