Understanding how the genomic instability that accompanies tumourdevelopment arises has been an important question for more than a century. Onepotential cause of such instability is defective chromosome segregation during mitosis. A cause of mitotic defects may lie in the acquisition of multiple mitoticspindle poles, through an increase in the number of centrosomes. Cancer cells frequently possess multiple centrosomes. DNA damaging treatments, or mutationsin key DNA repair genes, also lead to centrosome amplification. Here, we review current models for how cells may lose the normal controls on centrosome dupli-cation and acquire more than the normal number of these organelles. We alsodiscuss how genotoxic stresses may contribute to the dysregulation of centrosome duplication and how this process may be a contributory factor in cellulartransformation.