New insights into the magma storage and evolution at oceanic island volcanoes are now being achieved using remotely sensed space geodetic techniques, namely satellite radar interferometry. Differential radar interferometry is a technique tracking, at high spatial resolution, changes in the travel-time (distance) from the satellites to the ground surface, having wide applications in Earth sciences. Volcanic activity usually is accompanied by surface ground deformation. In many instances, modelling of surface deformation has the great advantage to estimate the magma volume change, a particularly interesting parameter prior to eruptions. Jointly interpreted with petrology, degassing and seismicity, it helps to understand the crustal magmatic systems as a whole. Current (and near-future) radar satellite missions will reduce the revisit time over global sub-aerial volcanoes to a sub-weekly basis, which will increase the potential for its operational use. Time series and filtering processing techniques of such streaming data would allow to track subsurface magma migration with high precision, and frequently update over vast areas (volcanic arcs, large caldera systems, etc.). As an example for the future potential monitoring scenario, we analyze multiple satellite radar data over El Hierro Island (Canary Islands, Spain) to measure and model surface ground deformation. El Hierro has been active for more than 2 years (2011 to present). Initial phases of the unrest culminated in a submarine eruption (late 2011 – early 2012). However, after the submarine eruption ended, its magmatic system still active and affected by pseudo-regular energetic seismic swarms, accompanied by surface deformation without resumed eruptions. Such example is a great opportunity to understand the crustal magmatic systems in low magma supply-rate oceanic island volcanoes. This new approach to measure surface deformation processes is yielding an ever richer level of information from volcanology to engineering and meteorological monitoring problems.