Conventional antitumor therapy is often complicated by the emergence of the so-called cancer stem cells (CSCs), which are characterized by low metabolic rates and high resistance to almost all existing therapies. Many problems of clinical oncology and a poor efficacy of current treatments in particular are ascribed to CSCs. Therefore, it is important to develop new compounds capable of eliminating both rapidly proliferating tumor cells and standard treatment-resistant CSCs. Curaxins have been demonstrated to manifest various types of antitumor activity. Curaxins simultaneously affect at least three key molecular cascades involved in tumor development, including the p53, NF-κB, and HSF1 metabolic pathways. In addition, studies of some curaxins indicate that they can inhibit the transcriptional induction of the genes for matrix metalloproteinases 1 and 8 (MMP1 and MMP8); the PI3K/AKT/mTOR signaling cascades; cIAP-1 (apoptosis protein 1) inhibitor activity; topoisomerase II; and a number of oncogenes, such as c-MYC and others. In vivo experiments have shown that the CSC population increases on gemcitabine monotherapy and is reduced on treatment with curaxin CBL0137. The data support the prospective use of FACT inhibitors as new anticancer drugs with multiple effects on cell metabolism.