Global coupled Earth System Models (ESMs) are important for predicting future climate conditions. To assess the quality and reliability of ESMs it is crucial to evaluate them against independent observations. In this thesis, land water storage-related variables from ESMs taking part in the Coupled Model Intercomparison Project Phases 5 and 6 (CMIP5 and CMIP6) are compared to observed terrestrial water storage (TWS) changes from the Gravity Recovery And Climate Experiment (GRACE) and its Follow-On (GRACE-FO) satellite missions. This thesis is the first study to provide a comprehensive assessment of ways in which space gravimetric measurements can be utilized to evaluate coupled ESMs, thereby tackling several challenges of such a comparison: Apart from external forcing data (e.g., the Sun's energy and greenhouse gas concentrations), CMIP ESMs are not constrained by observations, but evolve freely over time after being initialized. As a consequence, over long time spans they reproduce the climate variability in a statistical sense only, but not the exact timing of particular events. Thus, when analyzing (long-term) climate projections, a direct comparison to observed time series is not feasible, but higher order metrics as the linear trend, seasonal cycle, and interannual variability have to be utilized. Furthermore, discrepancies between observed TWS (full integrated water column, possibly superimposed by non-hydrological mass changes) and modeled TWS (representing only soil moisture and snow) regionally hamper the interpretation of results. In the comparison of a CMIP5 ESM ensemble with GRACE observations, simulated long-term wetting and drying trends are found to be consistent with observed TWS trends in several regions of the world (e.g., the Mediterranean, Southwestern United States, Central Asia). However, it is shown that interannual variations obscuring long-term trends in TWS can have a large influence over 30 years and more, which regionally prevents reliable conclusions about long-term wetting or drying from the short GRACE time series. In addition to long-term trends, the seasonal cycle and interannual variations of TWS in a CMIP6 multi-model ensemble are assessed with respect to present-day observed conditions. The model data are also analyzed for potential future changes of TWS variability, as these might be an important target for a future gravity mission with enhanced sensitivity. In contrast to long-term climate projections, decadal predictions can directly be compared on time series level, because they are frequently initialized with observed states of atmosphere and oceans. To this end, a GRACE-based TWS reconstruction is used to evaluate decadal climate predictions from CMIP5 and CMIP6 with the result that they provide skillful forecasts of TWS anomalies in markedly humid climates for two years and more into the future. Overall, this thesis highlights mutual benefits of climate modeling and geodesy: On the one hand, satellite-observed TWS has a great potential to validate the performance or to hint at shortcomings of ESMs for land water storage-related variables. On the other hand, ESM output can provide information on expected climate signals in TWS, which is important for future plans in space gravimetry aiming at the long-term monitoring of climate variations.