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