Abstract: Geosynchronous Earth Orbit Synthetic Aperture Radar (GEO SAR) runs in the height of 36000Km geosynchronous earth orbit, compared with traditional Low Earth Orbit (LEO) SAR (orbit height under 1000Km), GEO SAR has advantages of shorter repeat period, wider swath and so on. Firstly, the basic principle and state-of-art of GEO SAR in domestic and overseas are introduced. Secondly, coverage characteristic of GEO SAR is analyzed. Thirdly, the key problems of yaw steering and imaging on curved trajectory in GEO SAR are discussed in detail, and the corresponding primary solutions are presented in order to promote future research on GEO SAR.