The evolutionary history of chromosomes can be tracked by the comparative hybridization of large panels of bacterial artificial chromosome clones. This approach has disclosed an unprecedented phenomenon: 'centromere repositioning', that is, the movement of the centromere along the chromosome without marker order variation. The occurrence of evolutionary new centromeres (ENCs) is relatively frequent. In macaque, for instance, 9 out of 20 autosomal centromeres are evolutionarily new; in donkey at least 5 such neocentromeres originated after divergence from the zebra, in less than 1 million years. Recently, orangutan chromosome 9, considered to be heterozygous for a complex rearrangement, was discovered to be an ENC. In humans, in addition to neocentromeres that arise in acentric fragments and result in clinical phenotypes, 8 centromere-repositioning events have been reported. These 'real-time' repositioned centromere-seeding events provide clues to ENC birth and progression. In the present paper, we provide a review of the centromere repositioning. We add new data on the population genetics of the ENC of the orangutan, and describe for the first time an ENC on the X chromosome of squirrel monkeys. Next-generation sequencing technologies have started an unprecedented, flourishing period of rapid whole-genome sequencing. In this context, it is worth noting that these technologies, uncoupled from cytogenetics, would miss all the biological data on evolutionary centromere repositioning. Therefore, we can anticipate that classical and molecular cytogenetics will continue to have a crucial role in the identification of centromere movements. Indeed, all ENCs and human neocentromeres were found following classical and molecular cytogenetic investigations.