The chapter explores the problem of species spread in river systems. It introduces the basic quantitative tools for dealing with the topic: first advection-diffusion-reaction traditional equations, then more modern approaches via interacting particle systems and reaction random walks on graphs. The Mississippi-Missouri river system is once again taken as the epitomizing river network: the dramatic invasion of the zebra mussel (Dreissena polymorpha), seeded by the accidental discharge of ballast water from European cargo ships in the Great Lakes region, is studied via a multilayer network model, including not only hydrology but also the displacement due to anthropic activity. Advanced laboratory experiments are then described and modeled in which the response of the alga Euglena gracilis when exposed to controlled light fields is analyzed. This allows insight into the problem of how spatial resource availability shapes the invasion patterns of riverine populations. Finally, a thorough analysis of mixing and dispersion in river systems is the basic tool to tackle a problem of enormous interest, namely, estimating species distribution and abundance using environmental DNA.