Chromosome arm aneuploidies (CAAs) are pervasive in cancers. However, how they affect cancer development, prognosis and treatment remains largely unknown. Here, we analyse CAA profiles of 23,427 tumours, identifying aspects of tumour evolution including probable orders in which CAAs occur and CAAs predicting tissue-specific metastasis. Both haematological and solid cancers initially gain chromosome arms, while only solid cancers subsequently preferentially lose multiple arms. 72 CAAs and 88 synergistically co-occurring CAA pairs multivariately predict good or poor survival for 58% of 6977 patients, with negligible impact of whole-genome doubling. Additionally, machine learning identifies 31 CAAs that robustly alter response to 56 chemotherapeutic drugs across cell lines representing 17 cancer types. We also uncover 1024 potential synthetic lethal pharmacogenomic interactions. Notably, in predicting drug response, CAAs substantially outperform mutations and focal deletions/amplifications combined. Thus, CAAs predict cancer prognosis, shape tumour evolution, metastasis and drug response, and may advance precision oncology.