Streams, riparian areas, floodplains, alluvial aquifers and downstream waters (e.g., large rivers, lakes, oceans) are interconnected by longitudinal, lateral, and vertical fluxes of water, other materials and energy. Collectively, these interconnected waters are called fluvial hydrosystems. Physical and chemical connectivity within fluvial hydrosystems is created by the transport of nonliving materials (e.g., water, sediment, nutrients, contaminants) which either do or do not chemically change (chemical and physical connections, respectively). A substantial body of evidence unequivocally demonstrates physical and chemical connectivity between streams and riparian wetlands and downstream waters. Streams and riparian wetlands are structurally connected to downstream waters through the network of continuous channels and floodplain form that make these systems physically contiguous, and the very existence of these structures provides strong geomorphologic evidence for connectivity. Functional connections between streams and riparian wetlands and their downstream waters vary geographically and over time, based on proximity, relative size, environmental setting, material disparity, and intervening units. Because of the complexity and dynamic nature of connections among fluvial hydrosystem units, a complete accounting of the physical and chemical connections and their consequences to downstream waters should aggregate over multiple years to decades.