Free-flying space manipulator systems, in which robotic manipulators are mounted on a free-flying spacecraft, are envisioned for assembling, maintenance, repair, and contingency operations in space. Nevertheless, even for fixed-base systems, control of mechanical manipulators is a challenging task. This is due to strong nonlinearities in the equations of motion, and consequently different algorithms have been suggested to control end-effector motion or force, since the early research in robotic systems. In this paper, first a brief review of basic concepts of various algorithms in controlling robotic manipulators is introduced. Then, specific problems related to application of such systems in space and a microgravity environment is highlighted. Basic issues of kinematics and dynamics modeling of such systems, trajectory planning and control strategies, cooperation of multiple arm space free-flying robots, and finally, experimental studies and technological aspects of such systems with their specific limitations are discussed.