Aneuploidy is frequently associated with disease and developmental abnormalities. It is also a key characteristic of cancer. Several model systems have been developed to study the role of chromosomal instability and aneuploidy in tumorigenesis. The results are surprisingly complex, with the conditions sometimes promoting and sometimes inhibiting tumour formation. Here, we review the effects of aneuploidy and chromosomal instability in cells and model systems of cancer, propose a model that could explain these complex findings and discuss how the aneuploid condition could be exploited in cancer therapy.