Abstract Chromosomal instability (CIN) is the result of ongoing changes in the number (aneuploidy) and structure of chromosomes. CIN is induced by chromosome missegregation in mitosis and leads to karyotypic diversity within the cancer cell population, thereby adding to intratumor heterogeneity. Regardless of the overall pro-oncogenic function of CIN, its onset is typically detrimental for cell fitness and thus tumors must develop CIN-tolerance mechanisms in order to propagate. There is overwhelming genetic and functional evidence linking mutations in the tumor suppressor TP53 with CIN-tolerance. However, the pathways leading to p53 activation following chromosome missegregation remain controversial. Recently, additional mechanisms have been identified in CIN-surveillance, resulting in a more complex network of pathways acting independently or in cooperation with p53. Tolerance might also be achieved by modifying aspects of the cancer cell physiology in order to attenuate CIN or by adaptation to the consequences of aneuploid karyotypes. In this review, we summarize the current knowledge about p53-dependent and -independent mechanisms of CIN-tolerance in cancer, the adaptations observed in CIN cells buffering CIN levels, its consequences for cellular homeostasis, and the potential of exploiting these adaptations in order to design new cancer therapies.