Cancer stem cells (CSCs), including leukemia stem cells (LSCs), exhibit self-renewal capacity and differentiation potential and have the capacity to maintain or renew and propagate a tumor/leukemia. The initial isolation of CSCs/LSCs was in adult myelogenous leukemia, although more recently, the existence of CSCs in a wide variety of other cancers has been reported. CSCs, in general, and LSCs, specifically with respect to this review, are responsible for initiation of disease, therapeutic resistance and ultimately disease relapse. One key focus in cancer research over the past decade has been the development of therapies that safely eliminate the LSC/CSC population. One major obstacle to this goal is the identification of key mechanisms that distinguish LSCs from normal endogenous hematopoietic stem cells. An additional daunting feature that has recently come to light with advances in next-generation sequencing and single-cell sequencing is the heterogeneity within leukemias/tumors, with multiple combinations of mutations, gain and loss of function of genes, and so on being capable of driving disease, even within the CSC/LSC population. The focus of this review/perspective is on our work in identifying and validating, in both chronic myelogenous leukemia and acute lymphoblastic leukemia, a safe and efficacious mechanism to target an evolutionarily conserved signaling nexus, which constitutes a common "Achilles heel" for LSCs/CSCs, using small molecule-specific CBP/catenin antagonists.