As a complement and extension of the terrestrial network, the satellite network contributes to the acceleration of bridging the digital divide between different regions and can expand the coverage and service range of the terrestrial network. However, the satellite network features highly dynamic topology, long transmission delay, and limited on-board computing and storage capacity. Hence, various technical challenges, including routing scalability and transmission stability, are encountered in the organic integration of the satellite network and the terrestrial network and the construction of a global space-ground integrated network (SGIN). Considering the research challenges of SGIN, this study describes the international and domestic research progress of SGIN in terms of network architecture, routing, transmission, multicast-based content delivery, etc., and then discusses the research trends.