In this paper, we present the S-method-based approach to real-time motion compensation, image formation and image enhancement of moving targets in ISAR and SAR. This approach performs better than the Fourier transform by drastically improving images of fast, maneuvering targets. These advantages are a result of the S-method's ability to automatically compensate for quadratic and all even higher-order terms in phase. Thus, targets with constant acceleration will undergo full motion compensation and their point-scatterers will each be localized. It should be noted that the source of the quadratic term can come from not only acceleration, but also non-uniform rotational motion and the cosine term in wide-angle imaging. The method is also computationally simple, requiring only slight modifications to the existing Fourier transform-based algorithm.