Abstract : We model the ratio between gravity variation and ground vertical displacement that are due to a load located at the surface of a stratified, spherically symmetric and elastic earth model. Theoretical results are compared to numerical values found for different loads by using outputs of global models. We assess the resolution and the accuracy of the temporal variations of the water content in the ground estimated by the GRACE space gravity mission. These are compared to the seasonal variations predicted by several hydrological models. In Europe, the validation of the GRACE measurements by those of the GGP network gravimeters is based on a principal component analysis and highlights the drought of summer 2003. The gravitational coseismic and postseismic signatures of the Sumatra earthquake (2004) are extracted from the GRACE data. A modelling of the coseismic effect shows that the static response of the ocean must not be neglected.