The construction of large structures is one of the main development trends of the space exploration in the future, such as large space stations, large space solar power stations, and large space telescopes. It is one of important development tendency, which aims to make full use of space robots to assemble space structures autonomously in the aerospace industry. Considering that on-orbit assembly is an effective method to solve the problem of construction of large-scale spatial structures, it is necessary to motivate and facilitate the research of space robotics technologies for on-orbit assembly. Therefore, in this paper, the development status of space robot technology and the relevant space robot on-orbit assembly technology in recent decades are summarized. First, based on the space robot motion planning and assembly sequence planning, the development of space robot planning algorithms is introduced. For space robot assembly task, the space robot assembly method is summarized. From the control point of view, how to solve the vibration suppression and compliant assembly of on-orbit assembly is reviewed, which provides a reference for the autonomous intelligent assembly of space robots for large-scale structures in space. In order to simulate the space assembly scene on the ground, this paper introduces the development of ground verification experiments and provides ideas for the effective verification of space on-orbit assembly technology. In summary, though some of these problems have been satisfactorily solved in the past research, further research is still necessary in the future. Finally, it looks forward to the future research direction of space machine on-orbit assembly.