Previously regarded as the passive drains of watersheds, over the past 50 years, rivers have progressively been recognized as being actively connected with off‐channel environments. These connections prolong physical storage and enhance reactive processing to alter water chemistry and downstream transport of materials and energy. Here we propose river corridor science as a concept that integrates downstream transport with lateral and vertical exchange across interfaces. Thus, the river corridor, rather than the wetted river channel itself, is an increasingly common unit of study. Main channel exchange with recirculating marginal waters, hyporheic exchange, bank storage, and overbank flow onto floodplains are all included under a broad continuum of interactions known as “hydrologic exchange flows.” Hydrologists, geomorphologists, geochemists, and aquatic and terrestrial ecologists are cooperating in studies that reveal the dynamic interactions among hydrologic exchange flows and consequences for water quality improvement, modulation of river metabolism, habitat provision for vegetation, fish, and wildlife, and other valued ecosystem services. The need for better integration of science and management is keenly felt, from testing effectiveness of stream restoration and riparian buffers all the way to reevaluating the definition of the waters of the United States to clarify the regulatory authority under the Clean Water Act. A major challenge for scientists is linking the small‐scale physical drivers with their larger‐scale fluvial and geomorphic context and ecological consequences. Although the fine scales of field and laboratory studies are best suited to identifying the fundamental physical and biological processes, that understanding must be successfully linked to cumulative effects at watershed to regional and continental scales.