Whereas germline-inherited whole-chromosome aneuploidy has long been known to cause miscarriages and developmental abnormalities, somatically acquired aneuploidies have been observed in cancer cells and more recently also in cells of the normal liver and brain. Furthermore, aneuploidy is being increasingly reported in clinical isolates of pathogenic microbes such as fungi and parasites. Whereas many efforts have been devoted to the dissection of the molecular mechanisms that lead to aneuploidy, we have only recently started to investigate how aneuploidy alters the phenotypic makeup of a cell. Here we review recent evidence supporting the idea that aneuploidy is a large-effect mutation that introduces large changes in the cellular phenome. From a systems biology perspective, this can be explained by the extensive changes that aneuploidy brings about in both the transcriptome and the proteome of a cell. We further provide an evolutionary perspective on how aneuploidy-induced phenotypic variation may contribute to the exacerbation of human pathologies such as cancer and infectious diseases, by conferring selectable traits such as increased virulence and drug resistance.