Geography and the environment shape migrations, population bottlenecks and local movements of individuals, and thereby the patterns of genetic variation within the species. In this talk I will discuss how spatially explicit models, informed by past climate and ethnically diverse datasets of human genetic variation, can be used to infer how climate and vegetation affected the spread of anatomically modern humans out of Africa into Eurasia and the Americas and shaped genetic variation. During this process, humans encountered environments that differed dramatically from those where our species originated. This would have presented both challenges and opportunities, and set the stage for adaptation. However, the effects of specific adaptations on genetic variation can be confounded by the general demographic response to the new environments, such as local population bottlenecks. I will discuss how climate-informed spatial models can help to disentangle these factors by providing null models tailored to specific geographic contexts.