River networks modify material transfer from land to ocean. Understanding the factors regulating this function for different gaseous, dissolved, and particulate constituents is critical to quantify the local and global effects of climate and land use change. We propose the River Network Saturation (RNS) concept as a generalization of how river network regulation of material fluxes declines with increasing flows due to imbalances between supply and demand at network scales. River networks have a tendency to become saturated (supply ≫ demand) under higher flow conditions because supplies increase faster than sink processes. However, the flow thresholds under which saturation occurs depends on a variety of factors, including the inherent process rate for a given constituent and the abundance of lentic waters such as lakes, ponds, reservoirs, and fluvial wetlands within the river network. As supply increases, saturation at network scales is initially limited by previously unmet demand in downstream aquatic ecosystems. The RNS concept describes a general tendency of river network function that can be used to compare the fate of different constituents among river networks. New approaches using nested in situ high-frequency sensors and spatially extensive synoptic techniques offer the potential to test the RNS concept in different settings. Better understanding of when and where river networks saturate for different constituents will allow for the extrapolation of aquatic function to broader spatial scales and therefore provide information on the influence of river function on continental element cycles and help identify policy priorities.