Population genetics is central to our understanding of human variation, and by linking medical and evolutionary themes, it enables us to understand the origins and impacts of our genomic differences. Despite current limitations in our knowledge of the locations, sizes and mutational origins of structural variants, our characterization of their population genetics is developing apace, bringing new insights into recent human adaptation, genome biology and disease. We summarize recent dramatic advances, describe the diverse mutational origins of chromosomal rearrangements and argue that their complexity necessitates a re-evaluation of existing population genetic methods.