Surface water storage (SWS), the amount of freshwater stored in rivers/wetlands/floodplains/lakes, and its variations are key components of the water cycle and land surface hydrology, with strong feedback and linkages with climate variability. They are also very important for water resources management. However, it is still very challenging to measure and to obtain accurate estimates of SWS variations for large river basins at adequate time/space sampling. Satellite observations offer great opportunities to measure SWS changes, and several methods have been developed combining multisource observations for different environments worldwide. With the upcoming launch in 2022 of the Surface Water and Ocean Topography (SWOT) satellite mission, which will provide, for the first time, direct estimates of SWS variations with an unprecedented spatial resolution (~100 m), it is timely to summarize the recent advances in the estimates of SWS from satellite observations and how they contribute to a better understanding of large-scale hydrological processes. Here, we review the scientific literature and present major results regarding the dynamic of surface freshwater in large rivers, floodplains, and wetlands. We show how recent efforts have helped to characterize the variations in SWS change across large river basins, including during extreme climatic events, leading to an overall better understanding of the continental water cycle. In the context of SWOT and forthcoming SWS estimates at the global scale, we further discuss new opportunities for hydrological and multidisciplinary sciences. We recommend that, in the near future, SWS should be considered as an essential water variable to ensure its long-term monitoring.