Chronic myeloid leukemia (CML) is a cancer of the hematopoietic system that is initiated by a single genetic alteration (the BCR-ABL fusion gene or Philadelphia chromosome) and progresses in several phases: during the chronic phase the number of cells grows slowly and the fraction of immature cells is low. During the accelerated phase and blast crisis, the population of CML cells and the fraction of immature cells rises sharply. The mechanisms that drive the transition from the chronic phase to blast crisis are not understood, and the requirement of genetic instability and further mutations has been suggested. Using mathematical models, I describe a theory that can account for the transition from the chronic phase to blast crisis without the need to invoke further mutations. The transition to blast crisis can be explained solely by feedback mechanisms that regulate the patterns of stem cell division, in particular the occurrence of symmetric versus asymmetric cell division. The model also has implications for the outcome of Imatinib treatment. According to the model, treatment can lead to the low level persistence of CML stem cells without assuming that these cells are less susceptible to drug-mediated activity, and this might explain why disease tends to relapse after treatment discontinuation even in the absence of acquired drug resistance. Further, the model defines conditions when Imatinib treatment might lead to the eradication of CML, which is relevant in the context of recent data that show absence of relapse as long as two years after treatment cessation.