Chromosome instability (CIN) is the process that leads to aneuploidy, a known hallmark of human tumours for over a century. Nowadays, it is believed that CIN promotes tumorigenesis by shuffling the genome into a malignant order through translocations, amplifications, deletions (structural CIN), and gains and losses of whole chromosomes (numerical CIN or nCIN). The present review focuses on the causes and consequences of nCIN. Several roads can lead to nCIN, including a compromised spindle assembly checkpoint, cohesion defects, p53 deficiency and flawed microtubule–kinetochore attachments. Whereas the link between nCIN and tumorigenesis is becoming more evident, indications have emerged recently that nCIN can suppress tumour formation as well. To understand these paradoxical findings, novel reagents and more sophisticated mouse models are needed. This will provide us with a better understanding of nCIN and eventually with therapies that exploit this characteristic of human tumours.