Centromeric DNA evolves rapidly, ranging in size and complexity over several orders of magnitude. Traditional attempts at studying centromeres have left unexplained the causes underlying this complexity and rapid evolution. Instead of directly studying centromeric DNA sequence, our approach has been to study the proteins that epigenetically determine centromere identity. We have discovered that centromeric histones (CenH3s) have evolved under positive selection in multiple lineages, suggesting an involvement in recurrent genetic conflict. Our hypothesis is that 'centromere-drive' is the source of this conflict. Under this model, centromeres compete via microtubule attachments for preferential transmission in female meioses occurring in animals and plants. Since only one of four meiotic products will become the egg, this competition confers a selfish advantage to chromosomes that can make more microtubule attachments, resulting in runaway expansions of centromeric satellites. While beneficial to the 'driving' chromosome, these expansions can have deleterious effects on the fitness of an organism and of the species. CenH3s as well as other heterochromatin proteins have evolved under positive selection to suppress the deleterious consequences of 'centromere-drive' by restoring meiotic parity.