Synthetic aperture imaging ladar can offer centimeter-class resolution with a real aperture size of a few meters in a thousand kilometers theoretically. The range and azimuth resolution are obtained by pulse compressing technique of frequency modulation(FM)-chirped pulses and phase history. But restricted by tunable laser itself， the perfect FM-chirped pulses are impossible. The phase errors due to the nonlinear chirp should be compensated to ensure the resolution. International progress of synthetic aperture imaging ladar experiments is reviewed， with focus on compensation methods. Based on the comparison of the developed methods， the conclusion and prospect of nonlinear chirp compensation technology is given finally.