Treatment and understanding of BCR::ABL1-positive leukaemias is a precision medicine success story. Our appreciation of the BCR::ABL1 gene and resulting BCR::ABL1 oncoprotein in chronic myeloid leukaemia (CML) and Philadelphia chromosome-positive (Ph+) acute leukaemias, has led to treatment advances associated with exceptional improvements in patient outcomes with normal life expectancy for many patients with chronic phase (CP-)CML. However, despite these major therapeutic advances, the management of Ph+ leukaemias remains complex, with development of specific resistance mutations on treatment, as well as the need for lifelong therapy in most patients due to the persistence of CML stem cells despite prolonged tyrosine kinase inhibitors (TKIs) treatment. BCR::ABL1-specific TKIs are associated with chronic toxicities affecting quality-of-life in many patients but can also result in more serious pulmonary and cardiovascular complications. Dose optimisation is increasingly being used to manage side effects and maintain molecular response in CML patients. Here, we review the development of BCR::ABL1-specific TKIs from the discovery of imatinib in 1996 to the more recent second- and third-generation TKIs and emerging specifically targeting the ABL myristoyl pocket (STAMP) inhibitors. We will also evaluate the current evidence for treatment of BCR::ABL1-positive leukaemias, including TKI discontinuation in optimally responding CP-CML patients.