Radar can obtain high spatial resolution at large operating distances and its operation is largely independent from weather and lighting conditions. This makes it an important instrument in an ever-increasing number of applications requiring robust and reliable sensing of the environment. Due to the advancements in semiconductor technology and digital computation power, radar can obtain increasingly better position estimation accuracy, detection sensitivity, and target resolution. High-resolution imaging is an example of a rapidly advancing field of radar technology. Inverse synthetic aperture radar (ISAR) is an imaging technique that uses the motion of a target to obtain a high-resolution radar image of it. This paper presents a comprehensive review of past work and the state-of-the-art in ISAR imaging systems, algorithms, and applications. Starting from the early historical developments of simple monostatic range-Doppler imaging, we present the developments up to the current advanced spatially distributed imaging modalities and reconstruction algorithms. The list of references includes the most influential ISAR publications in the open literature up to early 2021.