Biological invasions are a threat to ecosystems across all biogeographical realms. Riparian habitats are considered to be particularly prone to invasion by alien plant species and, because riparian vegetation plays a key role in both aquatic and terrestrial ecosystems, research in this field has increased. Most studies have focused on the biology and autecology of invasive species and biogeographical aspects of their spread. However, given that hydrogeomorphological processes greatly influence the structure of riparian plant communities, and that these communities in turn affect hydrology and fluvial geomorphology, scant attention has been paid to the interactions between invasions and these physical processes. Similarly, relatively little research has been undertaken on competitive interactions between alien and native riparian plant species. Further research in these fields is necessary at a variety of spatial and temporal scales before the dynamics of riparian invasions, and their impacts, can be properly understood.