Allogeneic chimeric antigen receptor T (CAR T) cells can offer advantages over autologous T cell therapies, including the availability of “fit” cells for production, and elimination of risks associated with inadvertent transduction of leukemic blasts. However, allogeneic T cell therapies must address HLA barriers and conventionally rely on the availability of a suitable HLA‐matched donor if graft‐vs‐host‐disease and rejection effects are to be avoided. More recently, the incorporation of additional genome editing manipulations, to disrupt T cell receptor expression and address other critical pathways have been explored. Clinical trials are underway investigating non‐HLA matched T cells expressing anti‐CD19 CARs for the treatment of B cell acute lymphoblastic leukemia (B‐ALL) and anti‐CD123 CAR for acute myeloid leukemia (AML). Such approaches continue to be refined and improved to widen accessibility and reduce the cost of T cell therapies for a wider range of conditions.