Centromeres are highly distinctive genetic loci whose function is specified largely by epigenetic mechanisms. Understanding the role of DNA sequences in centromere function has been a daunting task due to the highly repetitive nature of centromeres in animal chromosomes. The discovery of a centromere devoid of satellite DNA in the domestic horse consolidated observations on the epigenetic nature of centromere identity, showing that entirely natural chromosomes could function without satellite DNA cues. Horses belong to the genus Equus which exhibits a very high degree of evolutionary plasticity in centromere position and DNA sequence composition. Examination of horses has revealed that the position of the satellite-free centromere is variable among individuals. Analysis of centromere location and composition in other Equus species, including domestic donkey and zebras, confirms that the satellite-less configuration of centromeres is common in this group which has undergone particularly rapid karyotype evolution. These features have established the equids as a new mammalian system in which to investigate the molecular organization, dynamics and evolutionary behaviour of centromeres.