Digital synthetic-aperture radar (SAR) imaging techniques have previously only been reported in the literature in a fragmentory manner. This article presents a comprehensive review of the theory of digital SAR imaging from Earth-orbiting satellites. The digital SAR imaging process is explained, including a discussion of various aspects which are specific to satelliteborne SAR. A number of relevant digital-processing techniques are reviewed and it is shown how these techniques may be applied to the processing of digital SAR data. The range migration problem is discussed and various techniques for overcoming it are presented. The paper should be useful not only to the designer of SAR processors, but also to the user of digital SAR data and images.