BCR-ABL tyrosine kinase inhibitors, such as imatinib (Gleevec) are highly effective in treating human Philadelphia chromosome-positive (Ph+) chronic myeloid leukaemia (CML) in chronic phase but not in terminal acute phase; acquired drug resistance caused mainly by the development of BCR-ABL kinase domain mutations prevents cure of the leukaemia. In addition, imatinib is ineffective in treating Ph+ B-cell acute lymphoblastic leukaemia (B-ALL) and CML blast crisis, even in the absence of the kinase domain mutations. This type of drug resistance that is unrelated to BCR-ABL kinase domain mutations is caused by the insensitivity of leukaemic stem cells to kinase inhibitors such as imatinib and dasatinib, and by activation of a newly-identified signalling pathway involving SRC kinases that are independent of BCR-ABL kinase activity for activation. This SRC pathway is essential for leukaemic cells to survive imatinib treatment and for CML transition to lymphoid blast crisis. Apart from BCR-ABL and SRC kinases, stem cell pathways must also be targeted for curative therapy of Ph+ leukaemia.