The global monitoring of volume transports of large rivers is a challenging technological problem with a number of important applications. It is highly desirable to use satellite-based remote sensing techniques for consistent worldwide measurements on a regular basis. While water level measurements in rivers with spaceborne altimeters have already been demonstrated a few years ago, instruments for routine current measurements from space have not been available until now. This will change with the advent of along-track interferometric synthetic aperture radars (along-track InSARs) on upcoming satellites such as the German TerraSAR-X, which is scheduled for launch in 2006. In this paper we evaluate the potential of such instruments for current measurements in rivers. We consider fundamental theoretical issues as well as existing InSAR data from the Shuttle Radar Topography Mission (SRTM) and numerical simulation results. We find that currents in the Elbe river estuary (Germany) can be derived from SRTM data quite well. A similar data quality is predicted for TerraSAR-X. We discuss the potential of TerraSAR-X for routine current measurements in rivers and propose the development of a comprehensive data synthesis system which combines water level and current data from satellites and other sources in such a way that a maximum amount of information on rivers is obtained.