Centromeres are essential loci in eukaryotes that are necessary for the faithful segregation of chromosomes in mitosis and meiosis. Centromeres organize the kinetochore, the protein machine that attaches sister chromatids or homologous chromosomes to spindle microtubules and regulates their disjunction. Centromeres have both genetic and epigenetic determinants, which can come into conflict in asymmetric female meiosis in seed plants and animals. The centromere drive model was proposed to describe this conflict and explain how it leads to the rapid evolution of both centromeres and kinetochores. Recent studies confirm key aspects of the centromere drive model, clarify its mechanisms, and implicate rapid centromere/kinetochore evolution in hybrid inviability between species.