As a space communication network for information delivery, satellite Internet has the characteristics of wide-area coverage and reliability, which makes it an important strategic infrastructure.In satellite Internet, the routing technologies were necessary for the global accessibility of information and the utilization of space resources, thus reviewing the routing technologies for satellite Internet was focused on.Considering that the routing strategy was based on system architecture, firstly, the routing technologies for single-layer and multi-layer satellite constellation systems were reviewed respectively.In addition, routing strategies often involved optimization issues, therefore, the existing research work from the perspectives of delay, bandwidth, packet loss rate, robustness, and the resource utilization was also classified and reviewed.Finally, the further research directions were recommended.