The branch of orbital robotics focuses on robotic activities in Earth orbit, in which on-orbit servicing, active debris removal, on-orbit assembly and astronaut support are among the tasks of greatest interest. This chapter includes a first introductory section, which describes the peculiarities and challenges related to these tasks. The following two sections focus mainly on dynamic modeling and control of free-flying robots. Different control modes are considered, from the free-floating mode, in which external actions are assumed to be absent, to the combined control mode, in which the robot arm and its base body, the satellite, are controlled as one system. The use of trajectory planning within the control loop is discussed and results from past and recent activities in orbit are presented. Some of the most recent developments in the topics discussed are also illustrated throughout the chapter.