In chronic myeloid leukemia (CML), neoplastic stem cells and/or their subclones exhibit resistance against BCR/ABL tyrosine kinase inhibitors (TKIs). Therefore, residual CML stem cells (subclones) in TKI-treated patients are a logical target of therapy, and their elimination is considered a major aim and clue in the development of curative treatment approaches. A number of different mechanisms may underly resistance of CML stem cells against TKIs and other targeted or/and conventional drugs, including stem cell quiescence, expression of drug-transporters, stem cell plasticity, BCR/ABL mutations, overexpression of BCR/ABL and BCR/ABL-independent signalling- and survival-molecules. In this article, possibilities to overcome stem cell resistance in CML by exploiting knowledge on molecular mechanisms that underly the 'stem cell escape' from drug therapy are discussed.