The development of resistance to chemotherapeutic agents is a frequent cause of treatment failure in acute myeloid and lymphocytic leukaemia. The mechanisms by which resistance develops in these patients are poorly understood, although a framework for their investigation has been provided by a range of studies using animal and human cell lines as model systems. In this review the basic concepts of drug resistance mechanisms are outlined, with special emphasis on studies using cells obtained from patients with resistant forms of leukaemia.