With the development trend of intelligent manufacturing, the production process of products is becoming more and more flexible. Human-robot collaboration with high flexibility and automation level has become a research hotspot of manufacturing industry. In product assembly, the assembly operation with high flexibility and complex operation still needs to be finished by human, while the robot has the advantages of good repeatability, high load and high accuracy. In time and/or space sharing environment, robots are used to assist workers in assembly, which will reduce ergonomic pressure and workload, and achieve complementary advantages. Based on these understandings, this paper summarizes the research of human-robot collaborative assembly with time-space sharing. This paper reviews the current research status of the four hot spots developed around by scholars in recent years, namely, task allocation for human-robot collaboration, intention recognition for human-robot collaboration, path planning for human-robot collaboration, and safety design for human-robot collaboration collaborative assembly system. The development trend of these four aspects is discussed and prospected.