BCR-ABL1 kinase-induced chronic myeloid leukemia in chronic phase (CML-CP) usually responds to treatment with ABL tyrosine kinase inhibitors (TKIs) such as imatinib, dasatinib, and nilotinib. In most patients TKIs reduce the leukemia cell load substantially, but some leukemia cells, for example leukemia stem cells (LSCs), are intrinsically refractory to TKIs. In addition, some patients who respond initially may later become resistant to TKIs due to accumulation of point mutations in BCR-ABL1 kinase. LSCs or their progeny, leukemia progenitor cells (LPCs), at some stage may acquire additional genetic changes that cause the leukemia to transform further to a more advanced blast phase (CML-BP), which responds poorly to treatment and is usually fatal. We postulate that LSCs and/or LPCs refractory or resistant to TKIs may be 'ticking time-bombs' accumulating additional genetic aberrations and eventually 'exploding' to generate additional TKI-resistant clones and CML-BP clones with complex karyotypes.