The most recent two decades have seen tremendous progress in the understanding and treatment of chronic myeloid leukemia, a disease defined by the characteristic Philadelphia chromosome and the ensuing BCR::ABL fusion protein. However, the biology of the disease extends beyond the Philadelphia chromosome into a nebulous arena of chromosomal and genetic instability, which makes it a genetically heterogeneous disease. The BCR::ABL oncoprotein creates a fertile backdrop for oxidative damage to the DNA, along with impairment of genetic surveillance and the favoring of imprecise error-prone DNA repair pathways. These factors lead to growing chromosomal instability, manifested as additional chromosomal abnormalities along with other genetic aberrations. This worsens with disease progression to accelerated and blast phase, and modulates responses to tyrosine kinase inhibitors. Treatment options that target the genetic aberrations that mitigate chromosome instability might be a potential area for research in patients with advanced phase CML.