Allogeneic cellular immunotherapies hold a great promise for cancer treatment owing to their potential cost-effectiveness, scalability and on-demand availability. However, immune rejection of adoptively transferred allogeneic T and natural killer (NK) cells is a substantial obstacle to achieving clinical responses that are comparable to responses obtained with current autologous chimeric antigen receptor T cell therapies. In this Perspective, we discuss strategies to confer cell-intrinsic, immune-evasive properties to allogeneic T cells and NK cells in order to prevent or delay their immune rejection, thereby widening the therapeutic window. We discuss how common viral and cancer immune escape mechanisms can serve as a blueprint for improving the persistence of off-the-shelf allogeneic cell therapies. The prospects of harnessing genome editing and synthetic biology to design cell-based precision immunotherapies extend beyond programming target specificities and require careful consideration of innate and adaptive responses in the recipient that may curtail the biodistribution, in vivo expansion and persistence of cellular therapeutics.