In recent years, synthetic aperture radars (SARs) have been widely applied in various fields due to their all-weather, day-and-night global imaging capabilities. As one of the most common types of antennas, the reflector antenna offers some advantages for spaceborne radars, including low cost, lightweight, high gain, high radiation efficiency, and low sidelobes. Consequently, spaceborne SAR systems based on reflector antennas exhibit significant potential. This paper reviews the main types and characteristics of reflector antennas, with particular attention to the structural configurations and feed arrangements of deployable reflector antennas in spaceborne SAR applications. Additionally, some emerging techniques, such as digital beamforming, staggered SAR, and SweepSAR based on reflector antennas, are examined. Finally, future development directions in this field are discussed, including high-resolution wide-swath imaging and advanced antenna deployment schemes.