Aneuploidy, chromosome stoichiometry that deviates from exact multiples of the haploid compliment of an organism, exists in eukaryotic microbes, several normal human tissues, and the majority of solid tumors. Here, we review the current understanding about the cellular stress states that may result from aneuploidy. The topics of aneuploidy-induced proteotoxic, metabolic, replication, and mitotic stress are assessed in the context of the gene dosage imbalance observed in aneuploid cells. We also highlight emerging findings related to the downstream effects of aneuploidy-induced cellular stress on the immune surveillance against aneuploid cells.