A more accurate assessment of the contemporary evolution of the Greenland ice sheet and its major drainage basins requires a close interaction between observational data and modeling. The main challenge when interpreting satellite and observational data is to separate the ice mass contribution from the contribution of postglacial isostatic rebound, to separate ice-sheet dynamic changes from interannual surface mass balance changes, and to separate long-term ice-dynamic changes from short-term flow fluctuations. Here we report from recent progress towards these goals within the DFG SPP 1257 project 'Assessing the current evolution of the Greenland ice sheet' from studies combining observational data with glaciological modeling. This comprises studies to reconstruct the surface mass balance of the Greenland ice sheet between 1866 and 2006, optical satellite data from ASTER to obtain surface velocities, modelled balance velocities, and simulations with a three-dimensional thermomechanical ice-sheet model. In combination with GRACE data, these studies are expected to contribute to an improved estimate of the present-day contribution of the Greenland ice sheet to global sea-level change and a better understanding of the various contributions to current ice mass changes and their associated uncertainties.