Temporally resolved, 3-dimensional surface elevation data provide valuable insight into glacier dynamics, e.g. glaciers surges: short periods of rapid acceleration and mass transport which can pose significant hazard potential. Particularly in remote locations, such hazards can develop unobserved by the downstream communities at risk. This paper demonstrates the relevance of single-pass InSAR missions with two examples: Glacier lake outburst floods (GLOFs) of Kyagar Glacier in the Chinese Karakorum and the AruCo twin glacier collapse in Tibet. Periodic surging of Kyagar Glacier causes GLOFs affecting communities over 500 km downstream. Near AruCo, the mysterious but catastrophic collapses of two neighboring glaciers were also preceded by surge-like processes. In both cases typical signs of glacier surging (unusual advance) were absent in satellite images, but TanDEM-X InSAR DEMs revealed characteristic, surface elevation changes. Here, we summarize which information can be gained from surface elevation data to assess surge-related hazard potentials and to understand the underlying processes.