Radio frequency interference (RFI) is a major issue in accurate remote sensing by a synthetic aperture radar (SAR) system, which poses a great hindrance to raw data collection, image formation, and subsequent interpretation process. This paper provides a comprehensive study of the RFI mitigation techniques applicable for an SAR system. From the view of spectrum allocation, possible terrestrial and spaceborne RFI sources to SAR system and their geometry are analyzed. Typical signal models for various RFI types are provided, together with many illustrative examples from real measured data. Then, advanced signal processing techniques for removing RFI are reviewed. Advantages and drawbacks of each approach are discussed in terms of their applicability. Discussion on the future trends are provided from the perspective of cognitive, integrated, and adaptive. This review serves as a reference for future work on the implementation of the most suitable RFI mitigation scheme for an air-borne or space-borne SAR system.