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In view of the increasing number of space objects, comprehensive high‐quality space surveillance becomes ever more important. Radar is a powerful tool that, in addition to detection and tracking of objects, also enables spatially high‐resolution imaging independent of daylight and most weather conditions. Together with the technique of Inverse Synthetic Aperture Radar (ISAR), very high‐resolution and distance‐independent two‐dimensional images can be obtained. However, advanced high‐performance radar imaging of space objects is a complex and demanding task, touching many technological and signal processing issues. Therefore, besides theoretical work, the Microwaves and Radar Institute of German Aerospace Center (DLR) has developed and constructed an experimental radar system called IoSiS (Imaging of Satellites in Space) for basic research on new concepts for the acquisition of advanced high‐resolution radar image products of objects in a low earth orbit. Based on pulse radar technology, which enables precise calibration and error correction, IoSiS has imaged space objects with a spatial resolution in the centimetre range, being novel in public perception and accessible literature. The goal of this paper is therefore to communicate and illustrate comprehensively the technological steps for the construction and successful operation of advanced radar‐based space surveillance. Besides the basic description of the IoSiS system design this paper outlines primarily useful theory for ISAR imaging of objects in space, together with relevant imaging parameters and main formulae. All relevant processing steps, necessary for very high‐resolution imaging of satellites in practice, are introduced and verified by simulation results. Finally, a unique measurement result demonstrates the practicability of the introduced processing steps and error correction strategies. [ABSTRACT FROM AUTHOR]