Rivers impact the well-being of humans and the environment. As they increasingly face planetary-scale stressors, it is critically important to monitor and understand rivers at the global scale. As the only synoptic resource for global primary data on rivers, satellite remote sensing has recently begun to provide unprecedented opportunities for the monitoring, understanding, and prediction of global river behaviour. Despite these advances, the role of satellite remote sensing in global river science has still not been fully explored. New satellite systems and algorithms will enable substantial improvements in river measurements, provide new answers to long-standing or newly emerging scientific questions, and eventually update basic knowledge of rivers to advance global river science. In this Review we explore how remote sensing has been used to study the world’s rivers, examine challenges and opportunities for further advancing our understanding of rivers using existing and upcoming sensors, and identify possible solutions and future research directions.