Chronic myeloid leukaemia (CML) is a myeloid neoplasm defined by the BCR/ABL oncoprotein that is considered essential for leukaemogenesis and accumulation of neoplastic cells. The BCR/ABL kinase inhibitor imatinib is an effective agent in most patients and can now be regarded as front-line therapy. Hence, intrinsic and acquired resistance to imatinib has been described and is an emerging challenge in clinical practice. While CML stem cells display primary resistance, stem cell subclones may, in addition, acquire imatinib-resistant mutants of BCR/ABL. Other factors that are considered to contribute to stem cell resistance include the genetic background, clonal evolution, additional biological features of subclones, gene amplifications, silencing of tumour suppressor genes and specific pharmacological aspects. In this article, mechanisms of resistance of CML (stem) cells against imatinib and other BCR/ABL inhibitors are discussed, together with strategies to overcome and/or to prevent resistance with available drugs or novel anti-leukaemic approaches.