In this work, the inverse kinematics of sixteen fundamental 6-DOF robot manipulators with offset wrist were solved analytically and numerically. Analytical and numerical techniques are the most common approaches for solving inverse kinematics problems. They are generally desired to be solved analytically in order to have complete solution and fast computation. This approach is also called as closed form solution and in the absence of it, numerical techniques are used for solving the inverse kinematics problem. As examples, the inverse kinematics solutions of RS (Scara robot), CS (cylindrical robot), and NN (spherical robot) robot manipulators with offset wrist were presented in this paper. Also, the inverse kinematics solution techniques for sixteen fundamental robot manipulators equipped with offset wrist were summarized in a table.