Invertebrate pest invasions and outbreaks are associated with high social, economic, and ecological costs, and their significance will intensify with an increasing pressure on agricultural productivity as a result of human population growth and climate change. New molecular genetic and genomic techniques are available and accessible, but have been grossly underutilized in studies of invertebrate pest invasions, despite that they are useful tools for applied pest management and for understanding fundamental features of pest invasions including pest population demographics and adaptation of pests to novel and/or changing environments. Here, we review current applications of molecular genetics and genomics in the study of invertebrate pest invasions and outbreaks, and we highlight shortcomings from the current body of research. We then discuss recent conceptual and methodological advances in the areas of molecular genetics/genomics and data analysis, and we highlight how these advances will further our understanding of the demographic, ecological, and evolutionary features of invertebrate pest invasions. We are now well equipped to use molecular data to understand invertebrate dispersal and adaptation, and this knowledge has valuable applications in agriculture at a time when these are critically required.