Twenty years of continuous Earth observation by satellite SAR have resulted in numerous new insights into active volcanism, including a better understanding of subsurface magma storage and transport, deposition of volcanic materials on the surface, and the structure and development of volcanic edifices. This massive archive of data has resulted in fundamental leaps in our understanding of how volcanoes work – for example, identifying magma accumulation at supposedly quiescent volcanoes, even in remote areas or in the absence of ground-based data. In addition, global compilations of volcanic activity facilitate comparison of deformation behavior between different volcanic arcs and statistical evaluation of the strong link between deformation and eruption. SAR data are also increasingly used in timely hazard evaluation thanks to decreases in data latency and growth in processing and analysis techniques. The existing archive of SAR imagery is on the cusp of being enhanced by a new generation of satellite SAR missions, in addition to ground-based and airborne SAR systems, which will provide enhanced temporal and spatial resolution, broader geographic coverage, and improved availability of data to the scientific community. Now is therefore an opportune time to review the contributions of SAR imagery to volcano science, monitoring, and hazard mitigation, and to explore the future potential for SAR in volcanology. Provided that the ever-growing volume of SAR data can be managed effectively, we expect the future application of SAR data to expand from being a research tool for analyzing volcanic activity after the fact, to being a monitoring and research tool capable of imaging a wide variety of processes on different temporal and spatial scales as those processes are occurring. These data can then be used to develop new models of how volcanoes work and to improve quantitative forecasts of volcanic activity as a means of mitigating risk from future eruptions.