For two decades, leukaemia stem cells (LSCs) in chronic myeloid leukaemia (CML) and acute myeloid leukaemia (AML) have been advanced paradigms for the cancer stem cell field. In CML, the acquisition of the fusion tyrosine kinase BCR-ABL1 in a haematopoietic stem cell drives its transformation to become a LSC. In AML, LSCs can arise from multiple cell types through the activity of a number of oncogenic drivers and pre-leukaemic events, adding further layers of context and genetic and cellular heterogeneity to AML LSCs not observed in most cases of CML. Furthermore, LSCs from both AML and CML can be refractory to standard-of-care therapies and persist in patients, diversify clonally and serve as reservoirs to drive relapse, recurrence or progression to more aggressive forms. Despite these complexities, LSCs in both diseases share biological features, making them distinct from other CML or AML progenitor cells and from normal haematopoietic stem cells. These features may represent Achilles' heels against which novel therapies can be developed. Here, we review many of the similarities and differences that exist between LSCs in CML and AML and examine the therapeutic strategies that could be used to eradicate them.