With the development of science and technology, redundant manipulators have attracted extensive attention from scholars. When the redundant manipulator completes the specified task, it is required to transform the task path into the trajectory of joints, in which continuous inverse mapping of nonlinear functions is required to solve to develop the inverse kinematics solution. The solving process is particularly important and complex, and related researchers have conducted a lot of research on it. In this paper, the methods of solving inverse kinematics of the redundant manipulator are classified, and various methods with different characteristics are summarized. Besides, the basic principles and research status of the analytical method, numerical method, intelligent algorithm, and corresponding sub-method are described respectively. Finally, the development trend and existing challenges of inverse kinematics are pointed out.