Biological invasions, the establishment and spread of non‐native species in new regions, can have extensive economic and environmental consequences. Increased global connectivity accelerates introduction rates, while climate and land‐cover changes may decrease the barriers to invasive populations spread. A detailed knowledge of the invasion history, including assessing source populations, routes of spread, number of independent introductions, and the effects of genetic bottlenecks and admixture on the establishment success, adaptive potential, and further spread, is crucial from an applied perspective to mitigate socioeconomic impacts of invasive species, as well as for addressing fundamental questions on the evolutionary dynamics of the invasion process. Recent advances in genomics together with the development of geographic information systems provide unprecedented large genetic and environmental datasets at global and local scales to link population genomics, landscape ecology, and species distribution modeling into a common framework to study the invasion process. Although the factors underlying population invasiveness have been extensively reviewed, analytical methods currently available to optimally combine molecular and environmental data for inferring invasive population demographic parameters and predicting further spreading are still under development. In this review, we focus on the few recent insect invasion studies that combine different datasets and approaches to show how integrating genetic, observational, ecological, and environmental data pave the way to a more integrative biological invasion science. We provide guidelines to study the evolutionary dynamics of invasions at each step of the invasion process, and conclude on the benefits of including all types of information and up‐to‐date analytical tools from different research areas into a single framework.