Evolutionary genomics has – in the last two decades – unearthed a rich history of population dynamics while studying species across the planet, including complex patterns of divergence, migration and admixture among differentiated groups. Yet genome-wide studies of selection often assume simple dynamics or aim to control for complex dynamics without explicitly modeling them. This prevents these rich historical insights from bearing on our understanding of past adaptive events in the organisms we study. Here, I will introduce several new methods we have developed to explicitly account for complex population dynamics while looking for loci with footprints of positive selection. These include programs that can use admixture graphs and latent mixed-membership models to pinpoint exactly where and when in the history of a species a particular selective event took place, while explicitly modeling migration and admixture processes. I will also discuss applications of these methods to new present-day and ancient genomic datasets, including hundreds of Viking, Bronze Age, Neolithic and Mesolithic human genomes sampled throughout Eurasia, as well as bovine and fish population datasets. Finally, I will talk about on-going research on modeling archaic adaptive introgression from Neanderthals and Denisovans into modern humans, using convolutional neural networks.