Aneuploidy—the karyotype state in which the number of chromosomes deviates from a multiple of the haploid chromosome set—is common in cancer, where it is thought to facilitate tumor initiation and progression. However, it is poorly tolerated in healthy cells: during development and tissue homeostasis, aneuploid cells are efficiently cleared from the population. It is still largely unknown how cancer cells become, and adapt to being, aneuploid. P53, the gatekeeper of the genome, has been proposed to guard against aneuploidy. Aneuploidy in cancer genomes strongly correlates with mutations in TP53, and p53 is thought to prevent the propagation of aneuploid cells. Whether p53 also participates in preventing the mistakes in cell division that lead to aneuploidy is still under debate. In this review, we summarize the current understanding of the role of p53 in protecting cells from aneuploidy, and we explore the consequences of functional p53 loss for the propagation of aneuploidy in cancer.