During the last 10 years, an increasing number of studies have explored evolutionary aspects ofbiological invasions. It is becoming increasingly clear that evolutionary processes play animportant role during the establishment of non-native species. Genetic drift during thecolonization process followed by strong selection imposed through a change in biotic conditionsand co-evolutionary disequilibrium set the conditions for rapid evolutionary change in introducedpopulations. Different hypotheses, which have been proposed to explain how evolutionary andgenetic processes, can facilitate invasiveness are explored and their relevance for fish invasions isdiscussed. Empirical evidence increasingly suggests that admixture after multiple introductions,hybridization between native and non-native species and enemy release can all catalyse theevolution of invasiveness. A number of studies also suggest that genetic bottlenecks mightrepresent less of genetic paradox than previously thought. Much of the theoretical developmentsand empirical evidence concerning the importance of evolution during biological invasions hasbeen provided from studies on invasive plants. Despite their prominence, fish invasions havereceived little attention from evolutionary biologists. Recent advances in population geneticanalysis such as non-equilibrium methods and genomic techniques such as microarray technologyprovide suitable tools to address such issues.