The majority of the world’s human population lives in towns and cities. High population densities mean that damage and disruption caused by natural disasters and other events have a much greater impact when urban areas are affected. Satellite remote sensing has the potential to play an important role in urban disaster monitoring and management, thanks to its relative immunity to disruption by terrestrial events. When data is required promptly and at short notice, Synthetic Aperture Radar (SAR) is of particular interest because of its ability to penetrate atmospheric conditions such as cloud and smoke. This thesis describes some recent contributions in the field of urban SAR, and in particular the exploitation of SAR amplitude images from metre-resolution satellite SAR systems such as TerraSAR-X and COSMO/SkyMed. An efficient curvilinear feature detection algorithm based on the Lindeberg scale-space ridge detector is introduced, and used for extraction of bright lines from SAR images. Two novel feature classification techniques for the detection of buildings are described, based on model selection: one supervised approach using local brightness and ridge strength statistics of bright line points, and one unsupervised approach using shape-dependent statistics of curvilinear features and priors derived from idealised building geometry. Finally, this thesis discusses the successful integration of these methods into an unsupervised tool for earthquake damage detection. The effectiveness of the models, algorithms and software tools is demonstrated and illustrated using SAR data from the COSMO/SkyMed constellation covering the 2009 earthquake in L’Aquila, Italy and the 2010 earthquake in Port-au-Prince, Haiti. The research described in this thesis provides the conceptual basis for a whole new approach to urban feature extraction, classification and change detection, using statistical models for the actual geometry of urban structures.