Aneuploidy describes the gain or loss of entire chromosomes or chromosome arms. Already more than 100 years ago, aneuploidy was described to be featured in cancer and it is known today to be present in 68-90 % of cancers, depending on tumour entity. Aneuploidy is implicated to affect cancer growth, therapy response and frequently affects prognosis. Chromosomal instability (CIN) is recognized as the main cause of aneuploidy and is characterised as the fluent process of gaining or losing chromosomes. Chromosomally instable cells need to be kept in check, or cleared, to prohibit the sampling of aneuploid karyotypes able to drive tumorigenesis. Of note, even aneuploid cancer cells often show CIN, a feature that promotes therapy related drug-resistance. Here, we review how CIN can be prevented or limited to spread by the induction of cell death and the relevance of different p53 responses triggered in response to mitotic perturbations to prohibit the formation of cancer driving aneuploidies.