Introduced species often exhibit changes in genetic variation, population structure, selection regime and phenotypic traits as they colonize and expand into new ranges. For these reasons, species invasions are increasingly recognized as promising systems for studying adaptive evolution over contemporary time scales. However, changes in phenotypic traits during invasion occur under non-equilibrium demographic conditions and may reflect the influences of prior evolutionary history and chance events, as well as selection. We briefly review the evidence for phenotypic evolution and the role of selection during invasion. While there is ample evidence for evolutionary change, it is less clear if selection is the primary mechanism. We then discuss the likelihood that stochastic events shift phenotypic distributions during invasion, and argue that hypotheses of adaptation should be tested against appropriate null models. We suggest two experimental frameworks for separating stochastic evolution from adaptation: statistically accounting for phenotypic variation among putative invasion sources identified by using phylogenetic or assignment methods and by comparing estimates of differentiation within and among ranges for both traits and neutral markers (Q(ST) vs. F(ST)). Designs that incorporate a null expectation can reveal the role of history and chance in the evolutionary process, and provide greater insights into evolution during species invasions.