The introduction of Abl tyrosine kinase inhibitors (TKI; that is, imatinib, dasatinib and nilotinib) as front-line therapy completely changed the course of chronic myelogenous leukemia (CML) to the point that most of the TKI-responsive newly diagnosed CML patients can be considered 'clinically' cured and their progression into blast crisis (BC) a rare event. However, a therapy for those patients who transform is still lacking, and TKIs do not eradicate CML at the stem cell level, therefore leaving a reservoir of cancer stem cells in a dormant stage. Thus, it is not surprising that the focus of CML research has shifted significantly toward the dissection of the mechanisms regulating the survival and self-renewal of TKI-resistant Philadelphia-positive leukemic chronic phase and BC stem cells, with the ultimate goal of developing small molecules capable of selectively killing leukemic but not normal hematopoietic stem cells, thereby achieving a 'biological' cure for this disease.