In this paper we briefly review the structure, performance and future requirements of space robots, and identify the scientific problems and key technologies needing further study. Based on their functions, we divided space robots into mechanical arm systems, robots with a supporting function and robots for in-orbit servicing. Specific attention is paid to the van der Waals mechanism, which enables the attractive force generated between two solid bodies using the technique inspired by the geckos array of attaching pads, and is the key technology that supports robots designed for micro-gravity condition for in-orbit servicing in space stations. Further studies on mechanical arm systems should focus on the high stiffness lightweight requirements by introducing new materials, design and manufacturing technologies, multibody dynamics of the mechanical arms, objects and stations, lubrication of the motion systems in a vacuum, microgravity, high-low temperatures, and cosmic radiation environments. Studies on robots with a support function need to pay attention to changes in astronauts physical and psychological behaviour in an enclosed, confined, microgravity environment, and ways to make the robots work positively through designing suitable configurations and auxiliary operations. The interdisciplinary questions related to advanced artificial intelligence, such as speech recognition, expression recognition and understanding natural language, also need be studied. The key technology needed for in-orbit servicing robots is a dry adhesive for robots operating under high and low temperatures, space radiation, and in a vacuum to realize stable contact between a station and robots.