Global Synthetic Aperture Radar (SAR) measurements made over the past decades provide insights into the lateral extent of magmatic domains, and capture volcanic process on scales useful for volcano monitoring. Satellite-based SAR imagery has great potential for monitoring topographic change, the distribution of eruptive products and surface displacements (InSAR) at subaerial volcanoes. However, there are challenges in applying it routinely, as would be required for the reliable operational assessment of hazard. The deformation detectable depends upon satellite repeat time and swath widths, relative to the spatial and temporal scales of volcanological processes. We describe the characteristics of InSAR-measured volcano deformation over the past two decades, highlighting both the technique’s capabilities and its limitations as a monitoring tool. To achieve this, we draw on two global datasets of volcano deformation: the Smithsonian Institution Volcanoes of the World database and the Centre for the Observation and Modelling of Earthquakes, Volcanoes and Tectonics volcano deformation catalogue, as well as compiling some measurement characteristics and interpretations from the primary literature. We find that a higher proportion of InSAR observations capture non-eruptive and non-magmatic processes than those from ground-based instrument networks, and that both transient (< month) and long-duration (> 5 years) deformation episodes are under-represented. However, satellite radar is already used to assess the development of extended periods of unrest and long-lasting eruptions, and improved spatial resolution and coverage have resulted in the detection of previously unrecognised deformation at both ends of the spatial scale (~ 10 to > 1000 km2). ‘Baseline’ records of past InSAR measurements, including ‘null’ results, are fundamental for any future interpretation of interferograms in terms of hazard‚ both by providing information about past deformation at an individual volcano, and for assessing the characteristics of deformation that are likely to be detectable (and undetectable) using InSAR. More than half of all InSAR deformation signals attributed to magmatic processes have sources in the shallow crust (< 5 km depth). While the depth distribution of InSAR-derived deformation sources is affected by measurement limitations, their lateral distribution provides information about the extent of active magmatic domains. Deformation is common (24% of all potentially magmatic events) at loci ≥5 km away from the nearest active volcanic vent. This demonstrates that laterally extensive active magmatic domains are not exceptional, but can comprise the shallowest part of trans-crustal magmatic systems in a range of volcanic settings.