With the rapid development of spacecraft rendezvous and proximity operation technology, the problem of orbital pursuit-evasion has gradually become a research hotspot in the aerospace field. From the perspective of dynamics and control, the research status of spacecraft orbital pursuit-evasion was reviewed. General form of the orbital pursuit-evasion problem model based on quantitative differential games was given, and various types of orbital pursuit-evasion problems were systematically sorted out. For the solution of pursuit and escape strategies, the advantages and disadvantages of various methods were analyzed for closed-loop strategy and open-loop strategy. Focusing on the combination of artificial intelligence algorithm and orbital pursuit and escape problem, the research status of orbital pursuit and escape strategy based on deep neural network and reinforcement learning was expounded. Regarding future prospects, development directions has been proposed, including the pursuit-evasion game situation analysis, the multi-spacecraft game control, the game dynamics and control under three-body problem.