The concept of the species has traditionally been the principal unit for the classification of the diversity of life. Although the conceptual and legal relevance of the idea of species is profound and wide ranging it is also increasingly evident that the concept of species is a significant oversimplification of the complex processes at work in nature. The growing body of evidence from genomic data, and other sources, indicates that interspecific hybridization plays a much more substantial role in evolution than had previously been appreciated and that speciation, the formation of new species, is likely a more gradual process than had been appreciated. In my dissertation work, I have applied whole genome sequencing and ancient DNA based techniques to examine the evolutionary relationship of two closely related species, polar bears (Ursus maritimus) and brown bears (Ursus arctos), which occupy substantially different ecological niches. This work is presented in a series of three papers that have contributed to reshaping scientific understanding of the relatedness of polar bears and brown bears and suggest that climate changes can profoundly impact the frequency of hybridization between these two species. I have also contributed to method development – in a fourth paper my coauthors and I developed a novel application of existing analysis tools to estimate the end point of the speciation process, the time at which all gene flow has ceased, from genomic data. Finally, in collaboration with my co-first author Axel Barlow and colleagues, I have examined the evolutionary relationship between polar and brown bears and their closest extinct relatives, the cave bears, which has revealed previously undocumented admixture between cave bears and brown bears and provides insights into the extent of diversity within the paleo-species groups of cave bear.