In this review article, we trace the history of events leading to the development of individual-based models (IBMs) to represent aquatic organisms in rivers and streams. As a metaphor, we present this history as a series of confluences between individual scientists (tributaries) sharing ideas. We describe contributions of these models to science and management. One iconic feature of river IBMs is the linkage between flow and the physical habitat experienced by individual animals, and the first model that focused on this linkage is briefly described. We continue by reviewing the contributions of riverine IBMs to eight broad areas of scientific inquiry. The first four areas include research to understand 1) the effects of flow regimes on fish populations, 2) species interactions (e.g., size-mediated competition and predation), 3) fish movement and habitat selection, and 4) contaminant and water quality impacts on populations. Next, we review research using IBMs 5) to guide conservation biology of imperiled taxa through population viability analysis, including research 6) to understand river fragmentation by dams and reconnection, 7) to understand genetic outcomes for riverine metapopulations, and 8) to anticipate the future effects of temperature and climate change. This rich body of literature has contributed to both theoretical insights (e.g., about animal behavior and life history) and applied insights (e.g., population-level effects of flow regimes, temperature, and the effects of hydropower and other industries that share rivers with aquatic biota). We finish by exploring promising branches that lie ahead in the braided, downstream channel that represents future river modeling research.