Leukemia is a many-sided molecular disorder that arises because of over expression of oncogenes, suppression of tumor suppressor genes, and chromosomal translocations. These chromosomal rearrangements are nonetheless among the many determinants that underlie transformation of cells from normal to a cancerous phenotype and predispose cells to refractoriness against interventions by reduced drug influx and substantial drug efflux. This review unfolds current understanding of BCR-ABL1 (break point cluster region-c-abl oncogene 1, non-receptor tyrosine kinase) signaling with a focus on apoptotic suppressive mechanisms and alternative approaches to chronic myeloid leukemia therapy.