Bone marrow transplantation (BMT) after supralethal cytoreductive therapy in the acute leukemias, chronic myelogenous leukemia (CML), and the lymphomas may be curative in 50% to 60% of patients. The donor may be a human leukocyte antigen (HLA) matched family member (allogeneic), an identical twin (syngeneic), or the patient (autologous). In general, the outcome is best in younger patients and those transplanted early in their disease (i.e., in the first remission for acute leukemia and in the chronic phase of the disease in CML). Solutions to the major problems of allogeneic BMT, such as graft-versus-host disease and viral infections, are being actively pursued. Syngeneic and autologous BMT avoids some of the above problems, but relapses appear to be greater. Despite this problem, a significant number of cures have been accomplished. Newer methods of purging autologous marrow and newer preparative regimens promise to reduce the problem of relapses.