Chimeric antigen receptor (CAR) T cell therapy has achieved unrivalled success in the treatment of B cell and plasma cell malignancies, with five CAR T cell products now approved by the US Food and Drug Administration (FDA). However, CAR T cell therapies for solid tumours have not been nearly as successful, owing to several additional challenges. Here, we discuss mechanisms of tumour resistance in CAR T cell therapy and the emerging strategies that are under development to engineer CAR T cells to overcome resistance.