Orbital robotics is receiving growing attention worldwide for applications in servicing and repositioning of partially or fully defective satellites. In this paper, we present the scope and main results of a four-year research project, which aimed at developing necessary robotic technologies for such applications. The scope is two-fold, since we address both the human-operated robotic operational mode, referred to in robotics as forcefeedback teleoperation, as well as the alternative autonomous mode, for the specific task of approaching and grasping a freetumbling target satellite. We present methodological developments and experimental as well as numerical validations in the fields of tele-communications, computer vision, robot and spacecraft control and system identification. The results of this work constitute important advances in the fundamental building blocks necessary for the orbital applications of interest.