Chronic myeloid leukemia stem cells (CML LSCs) are a rare and quiescent population that are resistant to tyrosine kinase inhibitors (TKI). When TKI therapy is discontinued in CML patients in deep, sustained and apparently stable molecular remission, these cells in approximately half of the cases restart to grow, resuming the leukemic process. The elimination of these TKI resistant leukemic stem cells is therefore an essential step in increasing the percentage of those patients who can reach a successful long-term treatment free remission (TFR). The understanding of the biology of the LSCs and the identification of the differences, phenotypic and/or metabolic, that could eventually allow them to be distinguished from the normal hematopoietic stem cells (HSCs) are therefore important steps in designing strategies to target LSCs in a rather selective way, sparing the normal counterparts.