This chapter introduces quaternionQuaternionrotation rotation, which is achieved by using a unit quaternion \(\mathsf {\boldsymbol{q}}\) to define the rotation. The vector to be rotated is represented using a pure quaternion \(\mathsf {\boldsymbol{p}}\) . To perform the rotation on \(\mathsf {\boldsymbol{p}}\) using \(\mathsf {\boldsymbol{q}}\) , the not so obvious operation of \(\mathsf {\boldsymbol{q}}\mathsf {\boldsymbol{p}}\mathsf {\boldsymbol{q}}^{-1}\) is required. Both algebraic and geometric approaches are used to explore why quaternions are used in this way for rotation. The geometric approach also provides an insight into the connection between rotations and reflections with quaternions. Further light is shed on the quaternion rotation by looking at both rectangularRectangular rotation and conical rotationsConical rotation. The ease with which rotations are combined using quaternions is shown to follow in a straightforward way from quaternion rotation using \(\mathsf {\boldsymbol{q}}\mathsf {\boldsymbol{p}}\mathsf {\boldsymbol{q}}^{-1}\) . The chapter concludes with details of how to convert from a rotation matrixRotation matrix to a quaternion.