T cells engineered to express chimeric antigen receptors (CARs) that are specific for tumour antigens have led to high complete response rates in patients with haematologic malignancies. Despite this early success, major challenges to the broad application of CAR-T cells as cancer therapies remain, including treatment-associated toxicities and cancer relapse with antigen-negative tumours. Targeting solid tumours with CAR-T cells poses additional obstacles because of the paucity of tumour-specific antigens and the immunosuppressive effects of the tumour microenvironment. To overcome these challenges, T cells can be programmed with genetic modules that increase their therapeutic potency and specificity. In this Review Article, we survey major advances in the engineering of next-generation CAR-T therapies for haematologic cancers and solid cancers, with particular emphasis on strategies for the control of CAR specificity and activity and on approaches for improving CAR-T-cell persistence and overcoming immunosuppression. We also lay out a roadmap for the development of off-the-shelf CAR-T cells.