Aneuploidy, or imbalanced chromosome number, has profound effects on eukaryotic cells. In humans, aneuploidy is associated with various pathologies, including cancer, which suggests that it mediates a proliferative advantage under these conditions. Here, we discuss physiological changes triggered by aneuploidy, such as altered cell growth, transcriptional changes, proteotoxic stress, genomic instability and response to interferons, and how cancer cells adapt to the changing aneuploid genome.