Different from terrestrial fixed communication networks, new challenges are brought to the design ofrouting protocols and algorithms for satellite Internet because of the characteristics of highly dynamic nodes,limited on-board processing capabilities and periodic changes of network topology in satellite networks.Therouting technology proposed by the academic community for satellite networks is sorted out comprehensivelyand the future research hotspots of satellite routing technology is given in this paper. Firstly, the architectureof the satellite network and the main routing protocols currently used in the satellite communication system areintroduced, and the routing problem of the satellite optical communication network is also briefly introduced.Secondly, the routing algorithms are classified into centralized satellite routing, distributed satellite routing andhybrid satellite routing according to the management method of satellite nodes and the routing table generationmethod.Later the representative results of various satellite routing methods are introduced and theiroptimization goals and applicable scenarios are summarized in detail. Then, how to choose the appropriatesatellite network scenarios and network requirements under different satellite network scenarios is summarized.Finally, the challenges faced by the current satellite routing technology and future research hotspots aredescribed, and the current mainstream satellite network simulation platforms are introduced in the appendix.