The use of tyrosine kinase inhibitors (TKIs) targeted against the BCR-ABL1 oncoprotein has proven remarkably successful in chronic myeloid leukemia (CML) and long-term survival has become a reality. Despite this outstanding progress, detection of minimal residual disease precludes therapy termination in most TKI-receiving patients. CML has thus turned into a chronic illness, raising concerns about long-term safety, medication adherence, and health care costs. Although treatment cessation may be feasible in few selected patients achieving deep molecular responses, a definitive cure remains elusive owing to the discovery that TKIs spare quiescent leukemic stem cells (LSC). Understanding mechanisms underlying LSC behavior in TKI-treated patients may provide important clues to develop an array of strategies that ensure the complete destruction of LSC reservoirs and thereby offer CML patients a definitive cure.