Genetic and genomic aberrations, including chromosome arm-level aneuploidies (CAAs), are a hallmark of cancer. However, how CAAs affect cancer development, prognosis and treatment largely remains unknown. Here, by analysing pan-cancer CAA landscapes, we uncover novel aspects of tumour evolution. Both haematological and solid cancers initially gain chromosome arms, while only solid cancers subsequently preferentially lose multiple arms. We also determine probable orders in which CAAs occur during tumour evolution and CAAs that predict tissue-specific metastasis. Additionally, we identify 72 CAAs and 88 synergistically co-occurring CAA pairs that multivariately predict good or poor survival for 58% of 6,977 patients. Whole-genome doubling has a negligible effect. Supervised machine learning, specifically, elastic net regression using 5-fold cross-validation, 988 cell lines, 788 genomic features and 386,293 IC50 values of 453 drugs, identifies 31 CAAs that robustly alter response to 56 chemotherapeutic drugs across cell lines representing 17 cancer types. We also uncover 1,024 potential synthetic lethal pharmacogenomic interactions. Notably, in predicting drug response, CAAs substantially outperform well-established cancer gene mutations and focal SCNAs combined. Thus, CAAs predict cancer prognosis, shape tumour evolution, metastasis and drug response, and have the potential to advance precision oncology.