Genetically engineered T cells are powerful new medicines, offering hope for curative responses in patients with cancer. Chimaeric antigen receptors (CARs) are a class of synthetic receptors that reprogram lymphocyte specificity and function. CARs targeting CD19 have demonstrated remarkable potency in B cell malignancies. Engineered T cells are applicable in principle to many cancers, pending further progress to identify suitable target antigens, overcome immunosuppressive tumour microenvironments, reduce toxicities, and prevent antigen escape. Advances in the selection of optimal T cells, genetic engineering, and cell manufacturing are poised to broaden T-cell-based therapies and foster new applications in infectious diseases and autoimmunity.