The climate of the Earth is changing. A consequence of this is observed at the polar regions such as Greenland, where the ice sheet is melting with an increasing rate. The unloading of ice causes the Earth to respond elastically in terms of uplift and an outward horizontal deformation of the crust. This motion can be measured by permanent Global Positioning System (GPS) receivers. Hence, the rates of crustal displacement are an indirect measure of the occurring mass changes. Currently, 55 GPS sites are located around the margin of the Greenland ice sheet, continuously providing information about the state of the ice sheet. However, the Earth is also adjusting viscoelastically to variations in the late Pleistocene ice sheets i.e. glacial isostatic adjustment (GIA). Observed rates of crustal displacement therefor contain signals from both past and present ice mass variations. Hence, to interpret the observed rates a separation of theses signals are needed. In this thesis, observed rates of crustal displacement are combined with modeled elastic rates to obtain constraints on the vertical displacement rate related to GIA. Observed rates are furthermore used to assess the local mass balance of Upernavik Isstrøm and Jakobshavn Isbræ. GIA is an important correction in gravity-based mass balance estimates. It is therefore important to obtain reliable GIA predictions. Observed rates of crustal displacement can be used to constrain the GIA response, assuming that the presentday response, can be accurately modeled and removed. Over a period of a few decades, the GIA rate is assumed to be constant. Hence, changes in the observed rate results from the present-day changes. Here, mass change grids, derived from Ice, Cloud,and land Elevation Satellite (ICESat) data from three overlapping time spans are used to estimate the modeled elastic displacement rates at five permanent GPS sites in Greenland (THU1, SCOR, QAQ1, KULU, and KELY). These rates are compared to observed rates, which are estimated in the same time spans. An agreement in the temporal behavior between the modeled elastic and observed displacement rates indicates, that the modeled elastic displacements are well captured. Based on this analysis, the GIA rates are estimated to -1 ± 0.6 mm/yr at KELY, 2 ± 0.7 mm/yr at SCOR, and 0.5 ± 0.5 mm/yr at QAQ1. At the sites KULU and THU2 the elastic displacement rates could not be accurately estimated. Gradients of crustal displacement rates near Upernavik Isstrøm and Jakobshavn Isbræ are modeled and compared to observed rates, to assess the mass balance of these glaciers. By considering displacement gradients, contributions from the mass loss of the rest of the ice sheet and GIA are reduced. Hence, gradients of crustal displacement roughly represent the local mass balance. Here, an agreement of 0.8 mm/yr or better is obtained. This indicates that the mass balances of these glaciers are well captured.