Fast crisis response after natural disasters, such as earthquakes and tropical storms, is necessary to support, for instance, rescue, humanitarian, and reconstruction operations in the crisis area. Therefore, rapid damage mapping after a disaster is crucial, i.e., to detect the affected area, including grade and type of damage. Thereby, satellite remote sensing plays a key role due to its fast response, wide field of view, and low cost. With the increasing availability of remote sensing data, numerous methods have been developed for damage assessment. This article gives a comprehensive review of these techniques focusing on multi-temporal SAR procedures for rapid damage assessment: interferometric coherence and intensity correlation. The review is divided into six parts: First, methods based on coherence; second, the ones using intensity correlation; and third, techniques using both methodologies combined to increase the accuracy of the damage assessment are reviewed. Next, studies using additional data (e.g., GIS and optical imagery) to support the damage assessment and increase its accuracy are reported. Moreover, selected studies on post-event SAR damage assessment techniques and examples of other applications of the interferometric coherence are presented. Then, the preconditions for a successful worldwide application of multi-temporal SAR methods for damage assessment and the limitations of current SAR satellite missions are reported. Finally, an outlook to the Sentinel-1 SAR mission shows possible solutions of these limitations, enabling a worldwide applicability of the presented damage assessment methods.