By studying invasive species, evolutionary geneticists have been able to simultaneously inform management strategies and quantify rapid evolution in the wild. The role of genomics in invasion science is increasingly recognised, and the growing availability of reference genomes for invasive species is paving the way for whole-genome resequencing studies in a wide range of systems. Here, we survey the literature to assess the application of whole-genome resequencing data in invasion biology. For some applications, such as the reconstruction of invasion routes in time and space, sequencing the whole genome of many individuals simply increases the accuracy of existing methods. In other cases, population genomic approaches such as haplotype analysis can permit entirely new questions to be addressed and new technologies to be applied. To date whole-genome resequencing has only been applied to a handful of invasive systems, but these studies have highlighted important roles for processes such as balancing selection and hybridization that allow invasive species to reuse existing adaptations and rapidly overcome the challenges of a foreign ecosystem. The use of genomic data does not constitute a paradigm shift per se, but by leveraging new theory, tools, and technologies, population genomics can provide unprecedented insight into basic and applied aspects of invasion science.