Despite the universal requirement for faithful chromosome segregation, eukaryotic centromeres are rapidly evolving. It is hypothesized that rapid centromere evolution represents an evolutionary arms race between selfish genetic elements that drive, or propagate at the expense of organismal fitness, and mechanisms that suppress fitness costs. Selfish centromere DNA achieves preferential inheritance in female meiosis by recruiting more effector proteins that alter spindle microtubule interaction dynamics. Parallel pathways for effector recruitment are adaptively evolved to suppress functional differences between centromeres. Opportunities to drive are not limited to female meiosis, and selfish transposons, plasmids and B chromosomes also benefit by maximizing their inheritance. Rapid evolution of selfish genetic elements can diversify suppressor mechanisms in different species that may cause hybrid incompatibility.