A model disease in many respects, chronic myelogenous leukemia (CML) has been called the pristine paradigm for molecularly targeted therapy. Bcr-Abl tyrosine kinase inhibitors (TKIs) have dramatically altered the therapeutic landscape of CML, so much so that many patients diagnosed in chronic phase and treated appropriately now enjoy a life expectancy similar to that of the general population. However, despite the enormous strides made in advancing therapy for this disease, it remains, for the most part, incurable except by allogeneic hematopoietic stem cell transplantation (HSCT). For patients, this means a lifelong commitment to daily TKI therapy. These agents are expensive, and not without side effects, making cure a highly desirable and worthwhile goal. Multiple studies have shown that in contrast to their impressive efficacy against proliferating CML cells, TKIs are unable to eradicate the tiny fraction of quiescent stem cells that are responsible for disease persistence and recurrence upon TKI discontinuation. This has fueled efforts to better understand CML stem cell biology and elucidate survival pathways unique to these cells, the targeted interruption of which could potentially synergize with Bcr-Abl TKIs to confer synthetic lethality while sparing normal hematopoietic stem cells (HSCs). The molecular pathogenesis of CML and mechanisms of resistance to TKIs are reviewed in detail elsewhere in this volume. In this chapter, we provide a brief overview of these topics, summarize key concepts relating to CML stem cell biology, and discuss strategies to effectively target this difficult-to-kill population that might one day result in a cure for CML.