The BCR-ABL1 oncogenic tyrosine kinase can transform pluripotent hematopoietic stem cells and initiate chronic myeloid leukemia in chronic phase (CML-CP), a myeloproliferative disorder characterized by excessive accumulation of mature myeloid cells. Patients in CML-CP usually respond to treatment with ABL1 tyrosine kinase inhibitors (TKIs) such as imatinib, though some patients who respond initially may become resistant later. CML-CP leukemia stem cells (LSCs) are intrinsically insensitive to TKIs and thus survive in the long term. These LSCs or their progeny may at some stage acquire additional genetic changes that cause the leukemia to transform further, from CML-CP to a more advanced phase, which has been subclassified as either accelerated phase (CML-AP) or blastic phase (CML-BP). CML-BP is characterized by a major clonal expansion of immature progenitors, which have either myeloid or lymphoid features. CML-BP responds poorly to treatment and is usually fatal. This review discusses the role of genomic instability leading to blastic transformation of CML and proposes some novel therapeutic approaches.