As it becomes easier to sequence multiple genomes from closely related species, evolutionary biologists working on speciation are struggling to get the most out of very large population genomic data sets. Such data hold the potential to resolve long-standing questions in evolutionary biology about the role of gene exchange in species formation. In principle, the new population genomic data can be used to disentangle the conflicting roles of natural selection and gene flow during the divergence process. However, there are great challenges in taking full advantage of such data, especially with regard to including recombination in genetic models of the divergence process. Current data, models, methods and the potential pitfalls in using them will be considered here.