River networks evolve as migrating drainage divides reshape river basins and change network topology by capture of river channels. We demonstrate that a characteristic metric of river network geometry gauges the horizontal motion of drainage divides. Assessing this metric throughout a landscape maps the dynamic states of entire river networks, revealing diverse conditions: Drainage divides in the Loess Plateau of China appear stationary; the young topography of Taiwan has migrating divides driving adjustment of major basins; and rivers draining the ancient landscape of the southeastern United States are reorganizing in response to escarpment retreat and coastal advance. The ability to measure the dynamic reorganization of river basins presents opportunities to examine landscape-scale interactions among tectonics, erosion, and ecology.