Space robotics is considered one of the most promising approaches for on-orbit servicing (OOS) missions such as docking, berthing, refueling, repairing, upgrading, transporting, rescuing, and orbital debris removal. Many enabling techniques have been developed in the past two decades and several technology demonstration missions have been completed. A number of manned on-orbit servicing missions were successfully accomplished but unmanned, fully autonomous, servicing missions have not been done yet. Furthermore, all previous unmanned technology demonstration missions were designed to service cooperative targets only. Robotic servicing of a non-cooperative satellite is still an open research area facing many technical challenges. One of the greatest challenges is to ensure the servicing spacecraft safely and reliably docks with the target spacecraft or capture the target to stabilize it for subsequent servicing. This is especially important if the target has an unknown motion and kinematics/dynamics properties. Obviously, further research and development of the enabling technologies are needed. To motivate and facilitate such research and development, this paper provides a literature review of the recently developed technologies related to the kinematics, dynamics, control and verification of space robotic systems for manned and unmanned on-orbit servicing missions.