Our vision of the cancer cell has dramatically changed since the discovery of proto-oncogenes, whose deregulation was proposed to mimic normal growth signalling. This notion, linking cancer to cell signalling pathways, has progressively led the way to the concept of the mutator phenotype, in which genetic instability plays an essential role in the onset of cancer. This then transformed cancer into a DNA repair disease. However, as foreseen decades ago by cytogeneticists, point mutations are not sufficient to give a full picture of the whole process. As a result, aneuploidy, rather than gene mutation, has been proposed as the explanation for the complex changes observed in cancer cells. The culprits were found among genes involved in the control of the cell division cycle, and work aimed at understanding the regulation of S phase and mitosis have yielded new insights into our understanding of cancer.