Human activities are accelerating rates of biological invasions and climate-driven range expansions globally, yet we understand little of how genomic processes facilitate the invasion process. Although most of the literature has focused on underlying phenotypic correlates of invasiveness, advances in genomic technologies are showing a strong link between genomic variation and invasion success. Here, we consider the ability of genomic tools and technologies to (i) inform mechanistic understanding of biological invasions and (ii) solve real-world issues in predicting and managing biological invasions. For both, we examine the current state of the field and discuss how genomics can be leveraged in the future. In addition, we make recommendations pertinent to broader research issues, such as data sovereignty, metadata standards, collaboration, and science communication best practices that will require concerted efforts from the global invasion genomics community.