The successful implementation of tyrosine kinase inhibitors (TKIs) for the treatment of chronic myeloid leukemia (CML) remains a flagship for molecularly targeted therapy in cancer. This focused review highlights critical elements of the underlying biology of CML and provides a summary of the molecular mechanisms that lead to TKI resistance: BCR-ABL1 mutation-based resistance and therapy escape through alternative pathway activation despite inhibition of BCR-ABL1 tyrosine kinase activity. We direct attention to the most current manifestations of these issues, including emergence of pan-TKI-resistant BCR-ABL1 compound mutants, new strategies for identification and therapeutic targeting of alternative pathways, and the exciting, controversial topic of cessation of TKI therapy leading to durable treatment-free remissions for a subset of patients. Further gains in our understanding of the biology of Philadelphia chromosome-positive (Ph-positive) leukemia and mechanisms of resistance to BCR-ABL1 TKIs will benefit patients and also provide a blueprint for similar discovery in other cancers.