Because the integrity of aquatic ecosystems is being challenged worldwide by invading species, there is a growing need to understand the invasion process and to predict the success and effects of invading species. Case histories of fish invasions in streams, lakes, and estuaries indicate that invading species and systems being invaded interact in idiosyncratic ways that are often hard to predict, largely because of the role of environmental variability in deter mining rite outcomes of invasions. We nevertheless present a conceptual model of aquatic invasions and a dozen empirically-derived rules that seem to govern most aquatic invasions. While these rules are limited in their usefulness, they do seem to have more predictive value than rules derived from community assembly theory. Copyright (C) 1996 Elsevier Science Limited