Chimeric antigen receptor (CAR) modified TCRab T cells are now available as authorised therapies for certain B cell malignancies, but the process of autologous harvest and generation of patient specific products is costly, with complex logistics and infrastructure requirements. Pre-manufactured banks of allogeneic donor derived CAR T cells could help widen applicability if the challenges of HLA mismatched T cell therapy can be addressed. Genome editing is being applied to overcome allogeneic barriers, most notably by disrupting TCRab to prevent graft versus host disease, and multiple competing editing technologies, including CRISPR/Cas9 and base editing, have reached clinical phase testing. Improvements in targeting and efficiency has unlocked applications against a wider range of blood malignancies with multiplexed editing incorporated to target HLA molecules, shared antigens and checkpoint pathways. Clinical trials will help establish safety profiles and determine the durability of responses, as well as the role of consolidation by allogeneic transplantation.