It has been known for more than a century that neoplastic cells often exhibit disturbances of the mitotic process, but the causes have only recently been thoroughly explored. In many cancers, a combination of cell cycle checkpoint deficiency and abnormal shortening of telomeres predisposes to unbalanced chromosome segregation at cell division and the development of complex genomic rearrangements. Shortening of telomeric repeats beyond normal limits leads to fusion of chromosome ends and the formation of chromatin bridges at anaphase. In turn, these bridges may trigger at least three types of chromosomes mutation: (1) structural rearrangements of chromosomes through extensive chromatin fragmentation beyond the centromeric sequences, typically leading to the formation of isochromosomes and whole-arm translocations, (2) loss of whole chromosomes through mechanical detachment from the mitotic spindle machinery, and (3) failure of cytokinesis, leading to polyploidisation and supernumerary centrosomes, which may in turn orchestrate multipolar spindle configurations at a subsequent mitosis. Anaphase bridging rarely hinders further survival of tumor daughter cells. In contrast, multipolar mitoses may lead to extensive reshuffling of chromosome copies that compromise further clonal expansion. The telomere-dependent instability can be partly counteracted by expression of telomerase during tumor progression, but genomic stabilisation is rarely, if ever, complete.