Dividing cells that experience chromosome mis-segregation generate aneuploid daughter cells, which contain an incorrect number of chromosomes. Although aneuploidy interferes with the proliferation of untransformed cells, it is also, paradoxically, a hallmark of cancer, a disease defined by increased proliferative potential. These contradictory effects are also observed in mouse models of chromosome instability (CIN). CIN can inhibit and promote tumorigenesis. Recent work has provided insights into the cellular consequences of CIN and aneuploidy. Chromosome mis-segregation per se can alter the genome in many more ways than just causing the gain or loss of chromosomes. The short- and long-term effects of aneuploidy are caused by gene-specific effects and a stereotypic aneuploidy stress response. Importantly, these recent findings provide insights into the role of aneuploidy in tumorigenesis.