Chimeric antigen receptor (CAR) T-cell therapy is a promising immunotherapy in haematological malignancies. However, the currently approved products are generated from autologous T cells that require orchestration of several logistically complex steps, which include patient eligibility, apheresis capability, complex manufacturing processes and shipping logistics. Use of third-party donor-derived (allogeneic) effector cells that allows the generation of 'off-the-shelf" CAR T cells (allo-CAR) could circumvent many of the problems associated with autologous CAR T-cell therapy. Several allogeneic products are entering clinical trials, and though early, the results look promising. The recognised potential benefits of allo-CAR do not come without significant challenges, that must be overcome for their widespread use. Alloreactivity, i.e. graft-versus-host disease (GVHD), and rejection of donor T cells is one of the major barriers, while other potential barriers include immunogenicity, unknown in vivo persistence, and CAR T-cell yield. In the present review, we provide a comprehensive review of the challenges associated with autologous CAR, the benefits and potential challenges associated with allo-CAR. Finally, we review the available platforms for allo-CAR for B-cell and plasma cell malignancies.