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Frequent high-resolution measurements of topography at active volcanoes can provide important information for assessing the distribution and rate of emplacement of volcanic deposits and their influence on hazard. At dome-building volcanoes, monitoring techniques such as LiDAR and photogrammetry often provide a limited view of the area affected by the eruption. Here, we show the ability of satellite radar observations to image the lava dome and pyroclastic density current deposits that resulted from 15 years of eruptive activity at Soufrière Hills Volcano, Montserrat, from 1995 to 2010. We present the first geodetic measurements of the complete subaerial deposition field on Montserrat, including the lava dome. Synthetic aperture radar observations from the Advanced Land Observation Satellite (ALOS) and TanDEM-X mission are used to map the distribution and magnitude of elevation changes. We estimate a net dense-rock equivalent volume increase of 108 ± 15M m3 of the lava dome and 300 ± 220M m3 of talus and subaerial pyroclastic density current deposits. We also show variations in deposit distribution during different phases of the eruption, with greatest on-land deposition to the south and west, from 1995 to 2005, and the thickest deposits to the west and north after 2005. We conclude by assessing the potential of using radar-derived topographic measurements as a tool for monitoring and hazard assessment during eruptions at dome-building volcanoes.