Genomes from thousands of ancient and modern genomes coupled with powerful new computational approaches have rewritten the evolutionary history of humans. It is now clear that gene flow among different hominins was a defining force in shaping the genetic variation of our species. We now that structural variants, differences in the presence, absence, location or direction of large segments of DNA, are prevalent in human genomes, underlying crucial phenotypic variation. We can now pinpoint recent ancestry of individual genomes using the minute amount of differences between them. Novel models of selection, genome evolution and demographic history provide a robust framework to investigate the observed variation. In this review session, I aim to introduce you some of the population genetics approaches that define this new era of human evolutionary history research. While doing so, I will highlight some of the caveats and unknowns in the field.