Allogeneic blood or bone-marrow transplantation (alloBMT) is a potentially curative treatment for a variety of haematological malignancies and nonmalignant diseases. Historically, human leukocyte antigen (HLA)-matched siblings have been the preferred source of donor cells owing to superior outcomes compared with alloBMT using other donors. Although only approximately one-third of patients have an HLA-matched sibling, nearly all patients have HLA-haploidentical related donors. Early studies using HLA-haploidentical alloBMT resulted in unacceptably high rates of graft rejection and graft-versus-host disease (GVHD), leading to high nonrelapse mortality and consequently poor survival. Several novel approaches to HLA-haploidentical alloBMT have yielded encouraging results with high rates of successful engraftment, effective GVHD control and favourable outcomes. In fact, outcomes of several retrospective comparative studies seem similar to those seen using other allograft sources, including those of HLA-matched-sibling alloBMT. In this Review, we provide an overview of the three most-developed approaches to HLA-haploidentical alloBMT: T-cell depletion with 'megadose' CD34⁺ cells; granulocyte colony-stimulating factor-primed allografts combined with intensive pharmacological immunosuppression, including antithymocyte globulin; and high-dose, post-transplantation cyclophosphamide. We review the preclinical and biological data supporting each approach, results from major clinical studies, and completed or ongoing clinical studies comparing these approaches with other alloBMT platforms.