Human groups show structured levels of genetic similarity as a consequence of factors such as geographical subdivision and genetic drift. Surveying this structure gives us a scientific perspective on human origins, sheds light on evolutionary processes that shape both human adaptation and disease, and is integral to effectively carrying out the mission of global medical genetics and personalized medicine. Surveys of population structure have been ongoing for decades, but in the past three years, single-nucleotide-polymorphism (SNP) array technology has provided unprecedented detail on human population structure at global and regional scales. These studies have confirmed well-known relationships between distantly related populations and uncovered previously unresolvable relationships among closely related human groups. SNPs represent the first dense genome-wide markers, and as such, their analysis has raised many challenges and insights relevant to the study of population genetics with whole-genome sequences. Here we draw on the lessons from these studies to anticipate the directions that will be most fruitful to pursue during the emerging whole-genome sequencing era.