Chronic myeloid leukaemia (CML) was the first leukaemia associated with a unique genetic abnormality, the Philadelphia chromosome. This results from a reciprocal translocation between chromosomes 9 and 22, which generates the BCR-ABL1 fusion gene encoding a constitutively active tyrosine kinase. The complex intracellular signalling initiated by BCR-ABL1 is responsible for disease development, and targeted tyrosine kinase inhibitors have been the most successful therapeutic advance in CML. In this chapter, we review the implications of BCR-ABL1 signalling in CML, how this knowledge revolutionized CML treatment, and discuss approaches to further improving therapeutic response by the targeting of leukaemic stem cells.