Genomic approaches are increasingly being used to study biological invasions. Here, we first analyse how high-throughput sequencing has aided our understanding of the mechanisms associated with biological invasions. These include the transport of propagules to pre-invaded areas, an exploration of the consequences of hybridisation during range expansions, and the pre- and post-invasion adaptation of colonising populations. We then explore how contemporary genomic methods have been used to probe and monitor the spread of non-indigenous species. More specifically, we focus on the detection of species richness from environmental samples, measures of quantitative traits that may promote invasiveness, analysis of rapid adaptation, and the study of phenotypic plasticity. Finally, we look to the future, exploring how genomic approaches will assist future biodiversity conservationists in their efforts to mitigate the spread and effects of biological invasions. Ultimately, although the use of genomic tools to study non-indigenous species has so far been rather limited, studies to date indicate that genomic tools offer unparalleled research opportunities to continually improve our understanding of marine biological invasions.