Transplants of hematopoietic stem cells from unrelated donors have become feasible for a growing population of patients with hematologic malignancy. More than 2,000 patients with acute and chronic leukemia, lymphoma, myeloma, and myelodysplasia are transplanted each year worldwide using marrow or blood stem cells from unrelated volunteers. Many patients have achieved complete immunologic tolerance and have become long-term survivors. The probability of finding a suitable donor has increased, because of the expansion of the network of registries containing more than 5 million HLA-typed donors worldwide. The selection of compatible donors has become more effective, thanks to the discovery of new HLA alleles and the development of precise and efficient HLA typing methods using DNA technology. Prophylaxis of viral and fungal infections has decreased morbidity and improved survival. The availability of more selective immunosuppressive agents provides the opportunity to decrease treatment-related toxicity and graft-versus-host disease.