Aneuploidy, whole chromosome or chromosome arm copy number imbalance, is a near-universal characteristic of human cancers. Here, we apply new genomic and experimental methods to study this little-understood phenomenon. In 10,522 cancer genomes from The Cancer Genome Atlas (TCGA), we found aneuploidy to be positively correlated with TP53 mutation, overall somatic mutation rate, and the expression of genes in proliferation-related pathways. Aneuploidy was anti-correlated with the expression of immune signaling genes, due to decreased leukocyte infiltrates in high-aneuploidy samples. Chromosome arm-level alterations occur in 78% of the TCGA cancers and show cancer-specific patterns; for example, loss of chromosome arm 3p is common in squamous cancers. We applied genome engineering to delete chromosome arm 3p in lung epithelial cells, causing decreased proliferation rescued in part by chromosome 3 duplication. This study defines genomic and phenotypic correlates of cancer aneuploidy and provides an experimental approach to study chromosome arm aneuploidy.