The introduction in 1998 of imatinib mesylate (IM), a first-generation BCR-ABL1 tyrosine kinase inhibitor (1G-TKI), to the treatment of chronic myelogenous leukemia patients in the chronic phase (CML-CP), significantly improved the prognosis of a previously incurable disease with a prognosed 5-year-long overall survival and progression-free survival of 91.7% and 94.7%, respectively. Long term follow-up studies of CML-CP patients verified the initial results, showing a 10-year overall response rate of 82-83.2%. In about one quarter of CML-CP patients, IM primary/secondary resistance or intolerance is diagnosed. After switching to a second generation BCR-ABL1 TKI (dasatinib, nilotinib, bosutinib), a complete cytogenetic response is obtained in only c. 50% of CML-CP patients. Also the frequency of deep molecular responses (DMR: MR 4.0 and MR 4.5 ) is relatively low. The results of 2G-TKI treatment are particularly unsatisfactory in patients carrying the TKI resistant BCR::ABL1 kinase domain mutants (BCR::ABL1 KD), especially BCR-ABL1 T315I. For this reason, other orally biocompatible compounds have been developed to target BCR-ABL T315I. One of these is ponatinib, which allows a major molecular response (MMR) and MR 4.5 to be obtained in 40% and 24% of severely TKIs-pretreated CML-CP patients, respectively. The latter represent a new class of allosteric BCR-ABL1 tyrosine kinase inhibitor [asciminib (ABL001)], specifically targeting the ABL myristoyl pocket of BCR-ABL tyrosine kinase. Its application in CML-CP patients previously treated with at least two TKIs resulted in an MMR rate and a MR 4.5 rate of 37.6% and 10.8%, respectively, at 96 weeks. The favorable asciminib response and tolerance profile was also confirmed in real--life conditions, even in subjects with previous ponatinib therapy failure (MR 4.5 in 10.5%). Recent data suggests that asciminib may be used in the first line or in combination with a 1G-or 2G-TKI. This latter strategy may enhance the rate of DMR obtained and increase the number of patients eligible for an attempt at treatment-free remission.