Chronic myeloid leukemia (CML) is a hematological stem cell disorder characterized by the excessive proliferation of the myeloid lineage. In its initial chronic phase, the myeloid progenitor cells expand and demonstrate apparently normal differentiation. The disease may then transform into the accelerated phase, usually associated with resistance to therapy, and finally, into acute leukemic progression phase - blast crisis. Abnormal myeloid cells produce progenitors, which have lost their ability to differentiate, but retain the capacity to proliferate. The molecular hallmark of CML is the Philadelphia chromosome, resulting from reciprocal chromosome translocation, t(9;22)(q34;q11), and containing the BCR/ABL fusion gene, producing the BCR/ABL protein with a constitutive tyrosine kinase activity. BCR/ABL-positive cells have faster growth and proliferation over their normal counterparts and are resistant to apoptosis. Introduction of imatinib (IM), a tyrosine kinase inhibitor, revolutionized the therapy of CML, changing it from a fatal disease into a chronic disorder. However, some patients show a primary resistance to IM, others acquire such resistance in the course of therapy. Therefore, a small number of leukemic stem cells retains self-renewal capacity under IM treatment. Because BCR/ABL is involved in many signaling pathways, some of them may be essential for resistance to IM-induced apoptosis. The PI3K/AKT, Ras and JAK/STAT signaling pathways are involved in resistance to apoptosis and can be activated by BCR/ABL. Therefore, they can be candidates for BCR/ABL-dependent pro-survival pathway(s), allowing a fraction of CML cells to withstand treatment with tyrosine kinase inhibitors.