The introduction of protein tyrosine kinase inhibitors (TKIs) in 1998 transformed the management of chronic myeloid leukemia (CML), leading to significantly reduced mortality and improved 5 year survival rates. However, the CML community is faced with several clinical issues that need to be addressed. Ten to 15% of CML patients are diagnosed in advanced phase, and small numbers of chronic phase (CP) cases experience disease progression each year during treatment. For these patients, TKIs induce only transient responses and alternative treatment strategies are urgently required. Depending on choice of first line TKI, approximately 30% of CML CP cases show suboptimal responses, due to a combination of poor compliance, drug intolerance, and drug resistance, with approximately 50% of TKI-resistance caused by kinase domain mutations and the remainder due to unknown mechanisms. Finally, the chance of successful treatment discontinuation is on the order of only 10-20% related to disease persistence. Disease persistence is a poorly understood phenomenon; all CML patients have functional Philadelphia positive (Ph+) stem and progenitor cells in their bone marrows and continue to express BCR-ABL1 by DNA PCR, even when in very deep remission and following treatment discontinuation. What controls the maintenance of these persisting cells, whether it is necessary to fully eradicate the malignant clone to achieve cure, and how that might be approached therapeutically are open questions.