In the last decades, population genetics has proved to be a powerful tool to study differentiation and divergence of species at different spatial and temporal scales. Classical molecular markers, mostly mitochondrial sequences and microsatellite loci, were successfully used to characterize the natural structure of populations, to identify the environmental factors favouring or impeding gene flow, and to understand the driving forces of genetic differentiation. In the context of current global changes, population genetics was also used to disentangle the demographic processes during invasions and expansions and to characterize dispersion patterns. These approaches have often highlighted the complexity and the sometimes counterintuitive nature of the on-going scenarios. The development of new model-based methods, such as approximate Bayesian computation (ABC), allows quantitative inferences and the explicit comparison of alternative scenarios. The recent advent of Next Generation Sequencing (NGS) technologies has revolutionized the field of population genetics, and now allows the development of genome-wide approaches even in non-model organisms. These major improvements provide most powerful tools to analyse the evolution of both neutral and adaptive genetic diversity. Taking the pine processionary moth as a case example, we will illustrate how population genetics and genomics can be used in forest entomology and bring valuable answers regarding invasion and expansion processes. In particular, we could identify signs of both diffusive dispersal and long-range movements during the expansion of this species in France, which suggests man-aided movements possibly linked to host plant trade. We will also show how genomic markers (RAD-seq) were developed and allowed to deeply explore a case of recent allochronic differentiation in Portugal, which resulted in the occurrence of a phenologically-shifted and highly divergent population for which specific management strategies must be applied.