Chromosomal instability (CIN), the persistent inability of a cell to faithfully segregate its genome, is a feature of many cancer cells. It stands to reason that CIN enables the acquisition of multiple cancer hallmarks; however, there is a growing body of evidence suggesting that CIN impairs cellular fitness and prevents neoplastic transformation. Here, we suggest a new perspective to reconcile this apparent paradox and share an unexpected link between aneuploidy and aging that was discovered through attempts to investigate the CIN-cancer relationship. Additionally, we provide a comprehensive overview of the function and regulation of the anaphase-promoting complex, an E3 ubiquitin ligase that mediates high-fidelity chromosome segregation, and describe the mechanisms that lead to whole-chromosome gain or loss. With this review, we aim to expand our understanding of the role of CIN in cancer and aging with the long-term objective of harnessing this information for the advancement of patient care.