Chronic myeloid leukemia (CML) is driven by a translocation event between chromosomes 9 and 22, leading to the formation of a constitutively active BCR-ABL1 oncoprotein. Approved tyrosine kinase inhibitors (TKIs) for CML inhibit BCR-ABL1 by competitively targeting its adenosine triphosphate (ATP)-binding site, which significantly improves patient outcomes. However, resistance to and intolerance of TKIs remains a clinical challenge. Asciminib is a promising investigational agent in development that allosterically targets BCR-ABL1 in a non-ATP-competitive manner. It binds to the ABL1 myristoyl-binding pocket and is effective against most ABL1 kinase domain mutations that confer resistance to ATP-competitive TKIs, including the T315I mutation. This review discusses unmet needs in the current CML treatment landscape, reports clinical data from asciminib trials that support the use of single-agent asciminib as third-line therapy and beyond, and explores the potential benefit of asciminib in combination with approved TKIs in earlier lines.