Polyploidy, an increased number of chromosome sets, is a surprisingly common phenomenon in nature, particularly in plants and fungi. In humans, polyploidy often occurs in specific tissues as part of terminal differentiation. Changes in ploidy can also result from pathophysiological events that are caused by viral-induced cell fusion or erroneous cell division. Tetraploidization can initiate chromosomal instability (CIN), probably owing to supernumerary centrosomes and the doubled chromosome mass. CIN, in turn, might persist or soon give way to a stably propagating but aneuploid karyotype. Both CIN and stable aneuploidy are commonly observed in cancers. Recently, it has been proposed that an increased number of chromosome sets can promote cell transformation and give rise to an aneuploid tumor. Here, we review how tetraploidy can occur and describe the cellular responses to increased ploidy. Furthermore, we discuss how the specific physiological changes that are triggered by polyploidization might be used as novel targets for cancer therapy.