Based on a detailed analysis of the signal model of the moving target, this thesis focuses on the theories and applications of ground moving target indicator (GMTI) and ground moving target imaging (GMTIm) algorithms in synthetic aperture radar/ ground moving target indicator (SAR/GMTI mode), wide-area surveillance ground moving target indication (WAS-GMTI) mode and frequency modulated continuous wave synthetic aperture radar (FMCW SAR) systems. The proposed algorithms can not only indicate and image fast-moving targets, but are also effective in the context of slow-moving target processing. The system design scheme combines the mechanical scanning mode and the airborne SAR system, while the azimuth moving target indication algorithm employs the additional range walk migration induced by FMCW SAR systems. In addition, the non-ideal errors that deteriorate the performance of GMTIm algorithms in real SAR data processing are discussed, and suitable compensation methods are provided.>.