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As an emerging technique to obtain remotely sensed data, geosynchronous synthetic aperture radar (GEOSAR) is still at the infant stage for the development of the basic theory although some prediction indicates that the first GEOSAR satellite would be in orbit around 2020. Before the launching, a series of challenges in GEOSAR must be addressed and the feasible solutions should be carried out. Thus, systematic analyses of challenges and solutions in GEOSAR are proposed here. In this paper, the GEOSAR has been studied through analyses of bi-static imaging geometry, signal model, Doppler characteristics, Doppler bandwidth and synthetic aperture time, and resolution evaluation of the GEOSAR imagery, in which both challenges and solutions are included.