diff --git a/python/damask/_rotation.py b/python/damask/_rotation.py
index 4b03e8f56..9fb83af7b 100644
--- a/python/damask/_rotation.py
+++ b/python/damask/_rotation.py
@@ -144,10 +144,91 @@ class Rotation:
         p = self.quaternion[...,1:]/np.linalg.norm(self.quaternion[...,1:],axis=-1,keepdims=True)
         return self.copy(rotation=Rotation(np.block([np.cos(pwr*phi),np.sin(pwr*phi)*p]))._standardize())
 
+    def __ipow__(self,pwr):
+        """
+        Raise quaternion to power (in-place).
+
+        Equivalent to performing the rotation 'pwr' times.
+
+        Parameters
+        ----------
+        pwr : float
+            Power to raise quaternion to.
+
+        """
+        return self**pwr
+
 
     def __mul__(self,other):
-        """Standard multiplication is not implemented."""
-        raise NotImplementedError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
+        """
+        Compose this rotation with other.
+
+        Parameters
+        ----------
+        other : damask.Rotation of shape(self.shape)
+            Rotation for comosition.
+
+        """
+        if isinstance(other,Rotation):
+            return self@other
+        else:
+           raise TypeError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
+
+    def __imul__(self,other):
+        """
+        Compose this rotation with other (in-place).
+
+        Parameters
+        ----------
+        other : damask.Rotation of shape(self.shape)
+            Rotation for comosition.
+
+        """
+        return self*other
+
+
+    def __truediv__(self,other):
+        """
+        Compose this rotation with inverse of other.
+
+        Parameters
+        ----------
+        other : damask.Rotation of shape (self.shape)
+            Rotation to inverse composition.
+
+        """
+        if isinstance(other,Rotation):
+            return self@~other
+        else:
+           raise TypeError('Use "R@b", i.e. matmul, to apply rotation "R" to object "b"')
+
+    def __itruediv__(self,other):
+        """
+        Compose this rotation with inverse of other (in-place).
+
+        Parameters
+        ----------
+        other : damask.Rotation of shape (self.shape)
+            Rotation to inverse composition.
+
+        """
+        return self/other
+
+
+    def apply(self,other):
+        """
+        Apply rotation to vector or second/forth order tensor field.
+
+        Parameters
+        ----------
+        other : numpy.ndarray of shape (...,3), (...,3,3), or (...,3,3,3,3)
+            Vector or tensor on which the rotation is apply
+
+        """
+        if isinstance(other,np.ndarray):
+            return self@other
+        else:
+            raise TypeError('Use "R1*R2" or "R1/R2", to compose rotations')
 
 
     def __matmul__(self,other):
diff --git a/python/tests/test_Rotation.py b/python/tests/test_Rotation.py
index bc6614fb9..5aed0bea2 100644
--- a/python/tests/test_Rotation.py
+++ b/python/tests/test_Rotation.py
@@ -974,6 +974,45 @@ class TestRotation:
         R_2 = Rotation.from_Euler_angles([360,0,0],degrees=True)
         assert np.allclose(R_1.misorientation(R_2).as_matrix(),np.eye(3))
 
+    def test_composition(self):
+        a,b = (Rotation.from_random(),Rotation.from_random())
+        c = a * b
+        a *= b
+        assert c == a
+
+    def test_composition_invalid(self):
+        with pytest.raises(TypeError):
+            Rotation()*np.ones(3)
+
+    def test_composition_inverse(self):
+        a,b = (Rotation.from_random(),Rotation.from_random())
+        c = a / b
+        a /= b
+        assert c == a
+
+    def test_composition_inverse_invalid(self):
+        with pytest.raises(TypeError):
+            Rotation()/np.ones(3)
+
+    def test_power(self):
+        a = Rotation.from_random()
+        r = (np.random.rand()-.5)*4
+        b = a**r
+        a **= r
+        assert a == b
+
+    def test_invariant(self):
+        R = Rotation.from_random()
+        assert R/R == R*R**(-1) == Rotation()
+
+    @pytest.mark.parametrize('vec',[np.ones(3),np.ones((3,3)), np.ones((3,3,3,3))])
+    def test_apply(self,vec):
+        assert (Rotation().from_random().apply(vec)).all()
+
+    def test_apply_invalid(self):
+        with pytest.raises(TypeError):
+            Rotation().apply(Rotation())
+
     @pytest.mark.parametrize('angle',[10,20,30,40,50,60,70,80,90,100,120])
     def test_average(self,angle):
         R = Rotation.from_axis_angle([[0,0,1,10],[0,0,1,angle]],degrees=True)