Centromeres are the chromosomal domains required to ensure faithful transmission of the genome during cell division. They have a central role in preventing aneuploidy, by orchestrating the assembly of several components required for chromosome separation. However, centromeres also adopt a complex structure that makes them susceptible to being sites of chromosome rearrangements. Therefore, preservation of centromere integrity is a difficult, but important task for the cell. In this review, we discuss how centromeres could potentially be a source of genome instability and how centromere aberrations and rearrangements are linked with human diseases such as cancer.