Chronic myeloid leukemia (CML), caused by constitutively active BCR-ABL1 fusion tyrosine kinase, has served as a paradigm for successful application of molecularly targeted cancer therapy. The development of the tyrosine kinase inhibitor (TKI) imatinib allows patients with CML to experience near-normal life expectancy. Specific point mutations that decrease drug binding affinity can produce TKI resistance, and secondand third-generation TKIs largely mitigate this problem. Some patients develop TKI resistance without known resistance mutations, with significant heterogeneity in the underlying mechanism, but this is relatively uncommon, with the majority of patients with chronic phase CML achieving long-term disease control. In contrast, responses to TKI treatment are short lived in advanced phases of the disease or in BCR-ABL1-positive acute lymphoblastic leukemia, with relapse driven by both BCR-ABL1 kinase-dependent and -independent mechanisms. Additionally, the frontline CML treatment with second-generation TKIs produces deeper molecular responses, driving disease burden below the detection limit for a greater number of patients. For patients with deep molecular responses, up to half have been able to discontinue therapy. Current efforts are focused on identifying therapeutic strategies to drive deeper molecular responses, enabling more patients to attempt TKI discontinuation.