Tyrosine kinase inhibitor (TKI) therapy targeting the BCR-ABL1 kinase is effective against chronic myeloid leukaemia (CML), but is not curative for most patients. Minimal residual disease (MRD) is thought to reside in TKI-insensitive leukaemia stem cells (LSCs) that are not fully addicted to BCR-ABL1. Recent conceptual advances in both CML biology and therapeutic intervention have increased the potential for the elimination of CML cells, including LSCs, through simultaneous inhibition of BCR-ABL1 and other newly identified, crucial targets.