Aneuploidy has been recognized as a hallmark of tumorigenesis for more than 100 years, but the connection between chromosomal errors and malignant growth has remained obscure. New evidence emerging from both basic and clinical research has illuminated a complicated relationship: despite its frequency in human tumours, aneuploidy is not a universal driver of cancer development and instead can exert substantial tumour-suppressive effects. The specific consequences of aneuploidy are highly context dependent and are influenced by a cell's genetic and environmental milieu. In this Review, we discuss the diverse facets of cancer biology that are shaped by aneuploidy, including metastasis, drug resistance and immune recognition, and we highlight aneuploidy's distinct roles as both a tumour promoter and an anticancer vulnerability.