Over the last 15 years studies on invasion genetics have provided important insights to unravel cryptic diversity, track the origin of colonizers and reveal pathways of introductions. Despite all these advances, to date little is known about how evolutionary processes influence the observed genetic patterns in marine biological invasions. Here, firstly we review the literature on invasion genetics that include samples from European seas. These seas constitute a wide array of unique water masses with diverse degrees of connectivity, and have a long history of species introductions. We found that only a small fraction of the recorded introduced species has been genetically analysed. Furthermore, most studies restrict their approach to describe patterns of cryptic diversity and genetic structure, with the underlying mechanisms involved in the invasion process being largely understudied. Secondly, we analyse how genetic, reproductive and anthropogenic traits shape genetic patterns of marine introduced species. We found that most studies reveal similar genetic diversity values in both native and introduced ranges, report evidence of multiple introductions, and show that genetic patterns in the introduced range are not explained by taxonomic group or reproductive strategy. Finally, we discuss the evolutionary implications derived from genetic patterns observed in non-indigenous species. We identify different scenarios that are determined by propagule pressure, phenotypic plasticity and pre-adaptation, and the effects of selection and genetic admixture. We conclude that there is a need for further investigations of evolutionary mechanisms that affect individual fitness and adaptation to rapid environmental change.