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With its temporal resolution of 10 days (five days with two satellites, and significantly more at high latitudes), its swath width of 290 km, and its 10 m and 20 m spatial resolution bands from the visible to the shortwave infrared, the European Sentinel-2 satellites have significant potential for glacier remote sensing, in particular mapping of glacier outlines and facies, and velocity measurements. Testing Level 1C commissioning and ramp-up phase data for initial sensor quality experiences, we find a high radiometric performance, but with slight striping effects under certain conditions. Through co-registration of repeat Sentinal-2 data we also find lateral offset patterns and noise on the order of a few metres. Neither of these issues will complicate most typical glaciological applications. Absolute geo-location of the data investigated was on the order of one pixel at the time of writing. The most severe geometric problem stems from vertical errors of the DEM used for ortho-rectifying Sentinel-2 data. These errors propagate into locally varying lateral offsets in the images, up to several pixels with respect to other georeferenced data, or between Sentinel-2 data from different orbits. Finally, we characterize the potential and limitations of tracking glacier flow from repeat Sentinel-2 data using a set of typical glaciers in different environments: Aletsch Glacier, Swiss Alps; Fox Glacier, New Zealand; Jakobshavn Isbree, Greenland; Antarctic Peninsula at the Larsen C ice shelf. [ABSTRACT FROM AUTHOR]