The water in Earth’s rivers propagates as waves through space and time across hydrographic networks. A detailed understanding of river dynamics globally is essential for achieving the accurate knowledge of surface water storage and fluxes to support water resources management and water-related disaster forecasting and mitigation. Global in situ information on river flows are crucial to support such an investigation but remain difficult to obtain at adequate spatiotemporal scales, if they even exist. Many expectations are placed on remote sensing techniques as key contributors. Despite a rapid expansion of satellite capabilities, however, it remains unclear what temporal revisit, spatial coverage, footprint size, spatial resolution, observation accuracy, latency time, and variables of interest from satellites are best suited to capture the space-time propagation of water in rivers. Additionally, the ability of numerical models to compensate for data sparsity through model-data fusion remains elusive. We review recent efforts to identify the type of remote sensing observations that could enhance understanding and representation of river dynamics. Key priorities include: (a) resolving narrow water bodies (finer than 50-100 m), (b) further analysis of signal accuracy versus hydrologic variability and relevant technologies (optical/SAR imagery, altimetry, microwave radiometry), (c) achieving 1-3 days observation intervals, (d) leveraging data assimilation and multi-satellite approaches using existing constellations, and (e) new variable measurement for accurate water flux and discharge estimates. We recommend a hydrology-focused, multi-mission observing system comprising: (1) a cutting-edge single or dual-satellite mission for advanced surface water measurements, and (2) a constellation of cost-effective satellites targeting dynamic processes.