The idea that within the bulk of leukemic cells there are immature progenitors which are intrinsically resistant to chemotherapy and able to repopulate the tumor after treatment is not recent. Nevertheless, the term leukemia stem cells (LSCs) has been adopted recently to describe these immature progenitors based on the fact that they share the most relevant features of the normal hematopoetic stem cells (HSCs), i.e. the self-renewal potential and quiescent status. LSCs differ from their normal counterparts and from the more differentiated leukemic cells regarding the default status of pathways regulating apoptosis, cell cycle, telomere maintenance and transport pumps activity. In addition, unique features regarding the interaction of these cells with the microenvironment have been characterized. Therapeutic strategies targeting these unique features are at different stages of development but the reported results are promising. The aim of this review is, by taking acute myeloid leukemia (AML) as a bona fide example, to discuss some of the mechanisms used by the LSCs to survive and the strategies which could be used to eradicate these cells.