Since the late 1800s, we have known that cancer cells often missegregate chromosomes during cell division. This phenomenon, known as chromosome instability, leads to aneuploidy, i.e., an abnormal chromosome number. Consistently, the vast majority of human tumours are aneuploid. However, mutations in genes that encode regulators of chromosome segregation are remarkably rare. This observation has puzzled cancer researchers for decades. We have shown that rescuing chromosome instability in vivo delays cancer development and alleviates tumour burden in mice. This work, along with research from other laboratories, has led to the proposal of the “oncogene-induced mitotic stress model”. This model constitutes a mechanistic framework that provides an explanation for the long-standing paradox of how cancer cells become aneuploid in the absence of mutations in chromosome segregation genes.