Loss or gain of chromosomes is associated with many cancer cells. This property, called chromosome instability, might arise from a lesion in the chromosome segregation machinery. Essential for chromosome segregation are the proper connection of microtubules to kinetochores, and the synchronous segregation of sister chromatids in anaphase. Accuracy of these processes is ensured by two sophisticated machineries called the correction mechanism and the spindle assembly checkpoint. Here we outline the current understanding of the underlying mechanisms, and highlight recent challenging experiments to address how chromosome segregation failure might relate to tumorigenesis. Understanding these mechanisms may lead to the discovery of new and improved anticancer therapies.