The influence of spatial processes on diversity and community dynamics is generally recognized in ecology and also applied to conservation projects involving forest and grassland ecosystems. Riverine ecosystems, however, have been for a long time viewed from a local or linear perspective, even though the treelike branching of river networks is universal. River networks (so-called dendritic networks) are not only structured in a hierarchic way, but the dendritic landscape structure and physical flows often dictate distance and directionality of dispersal. Theoretical models suggest that the specific riverine network structure directly affects diversity patterns. Recent experimental and comparative data are supporting this idea. Here, I provide an introduction on theoretical findings suggesting that genetic diversity, heterozygosity and species richness are higher in dendritic systems compared to linear or two-dimensional lattice landscapes. The characteristic diversity patterns can be explained in a network perspective, which also offers universal metrics to better understand and protect riverine diversity. I show how appropriate metrics describing network centrality and dispersal distances are superior to classic measures still applied in aquatic ecology, such as Strahler order or Euclidian distance. Finally, knowledge gaps and future directions of research are identified. The network perspective employed here may help to generalize findings on riverine biodiversity research and can be applied to conservation and river restoration projects.