Hydrological models and the data derived from the Gravity Recovery and Climate Experiment (GRACE) satellite mission have been widely used to study the variations in terrestrial water storage (TWS) over large regions. However, both GRACE products and model results suffer from inherent uncertainties, calling for the need to make a combined use of GRACE and models to examine the variations in total TWS and their individual components, especially in relation to natural and human-induced changes in the terrestrial water cycle. In this study, we use the results from two state-of-the-art hydrological models and different GRACE spherical harmonic products to examine the variations in TWS and its individual components, and to attribute the changes to natural and human-induced factors over large global river basins. Analysis of the spatial patterns of the long-term trend in TWS from the two models and GRACE suggests that both models capture the GRACE-measured direction of change, but differ from GRACE as well as each other in terms of the magnitude over different regions. A detailed analysis of the seasonal cycle of TWS variations over 30 river basins shows notable differences not only between models and GRACE but also among different GRACE products and between the two models. Further, it is found that while one model performs well in highly-managed river basins, it fails to reproduce the GRACE-observed signal in snow-dominated regions, and vice versa. The isolation of natural and human-induced changes in TWS in some of the managed basins reveals a consistently declining TWS trend during 2002-2010, however; significant differences are again obvious both between GRACE and models and among different GRACE products and models. Results from the decomposition of the TWS signal into the general trend and seasonality indicate that both models do not adequately capture both the trend and seasonality in the managed or snow-dominated basins implying that the TWS variations from a single model cannot be reliably used for all global regions. It is also found that the uncertainties arising from climate forcing datasets can introduce significant additional uncertainties, making direct comparison of model results and GRACE products even more difficult. Our results highlight the need to further improve the representation of human land-water management and snow processes in large-scale models to enable a reliable use of models and GRACE to study the changes in freshwater systems in all global regions.