The introduction of tyrosine kinase inhibitor treatment for CML marks one of the major success stories in the recent history of medicine. However, eradication of disease is almost never attained, because, unlike the vast majority of more differentiated cells, leukemic stem cells withstand TKIs, necessitating life-long treatment. Besides, although a relatively infrequent event under treatment with TKIs, refractory leukemic stem cells may sometimes give rise to disease transformation. In this article, we will review the definitions of CML stem cells, explain how BCR-ABL induces perturbations of critical signal transduction pathways and summarize specific characteristics that cause refractoriness of CML stem cells against TKIs. Furthermore, events that are responsible or related to transformation of the disease into blast crisis will be discussed and new research directions that should lead to successful ways to attack leukemic stem cells are proposed.