Ship surveillance is important for maritime security and safety. It plays important roles in many applications including ocean environment monitoring, search and rescue, anti-piracy and military reconnaissance. Among various sensors used for maritime surveillance, space-borne Synthetic Aperture Radar (SAR) is valued for its high resolution over wide swaths and all-weather working capabilities. However, the state-of-the-art algorithms for ship detection and identification do not always achieve a satisfactory performance. With the rapid development of space-borne Automatic Identification System (AIS), near real-time and global surveillance has become feasible. However, not all ships are equipped with or operate AIS. Space-borne SAR and AIS are considered to be complementary, and ship surveillance using an integrated combination has attracted much attention. In order to summarize the achievements and present references for further research, this paper attempts to explicitly review the developments in previous research as the basis of a brief introduction to space-borne SAR and AIS.