Patients with acute leukaemia have normal or near normal numbers of haemopoietic stem cells in their marrow at diagnosis. Remission is achieved when the administration of cytotoxic drugs eradicates the bulk of the leukaemic population while sparing normal haemopoiesis. The mechanism by which chemotherapy seems to act in this selective manner is essentially unknown. Nevertheless, remission rates of 80-95% can be achieved in children and in 50-80% of adults with acute leukaemia. Attempts to cure patients in remission may entail either "continuing curative chemotherapy" or "supralethal" doses of chemoradiotherapy followed by autologous or allogeneic bone marrow transplantation. The relative merits of these different methods remain highly controversial but chemotherapy is usually the preferred method of continuing treatment for children with acute lymphoblastic leukaemia in first remission; and allogeneic transplantation is recommended for younger adults with acute myeloid leukaemia who have suitable HLA-identical sibling donors. The role of autografting is still experimental. Patients with chronic myeloid leukaemia can achieve long term remission and probably cure following allogeneic bone marrow transplantation but the resultant risks of mortality are still appreciable. Chronic lymphocytic leukaemia currently remains incurable.