Evolution greatly impacts the outcomes of biological invasions. In our review, we review such evolutionary processes, with an emphasis on tree invasions, and place them in the context of a unified framework for biological invasions. The processes and mechanisms described are pre-introduction evolutionary history, sampling effect, founder effect, genotype-by-environment interactions, admixture, hybridization, polyploidization, rapid evolution, epigenetics, and second-genomes. By understanding the mechanisms underlying invasion success, researchers will be better equipped to predict, understand, and manage biological invasions.