Chronic myeloid leukemia (CML) is sustained by a clonally amplified population of Bcr Abl-positive pluripotent stem cells. Persistence of a large, functionally intact yet suppressed residual normal hematopoietic stem cell population in most patients with CML has made it possible to aim at the development of curative therapies. However, achieving this goal requires the identification of agents that will eradicate the leukemic stem cell population. Several potent Bcr-Abl-targeted drugs have now been introduced into clinical practice with remarkable effects. Nevertheless, accumulating data indicate that the leukemic CML stem cells in patients with chronic phase CML are less responsive to these agents than the bulk of the neoplastic cells. In this article, we review emerging evidence that CML stem cells have a number of unusual properties that underlie their relative insensitivity to treatment, including those that specifically target the Bcr-Abl oncoprotein. The biology of the neoplastic stem cells in patients with CML is clearly important to the future attainment of cures and might also prove a paradigm relevant to other types of malignancies that are sustained by transformed stem cell populations.