Over 50 years of experience in free radical biology and medicine shows that normal cells of healthy mammals are characterized by a low steady-state level of reactive oxygen species (ROS) and a constant (reference) level of reducing equivalents. A lasting increase of ROS above the critical level leads to permanent oxidative stress in the cells. This could cause genomic instability and mutations, which are responsible for adaptation of cells to oxidative stress and their survival in an oxidative environment. In turn, these events could provoke malignancy. It is widely accepted that the balance between ROS and reducing equivalents in cells and tissues determines their redox status. The evaluation of tissue redox status has great diagnostic potential in cancer, as well as prognostic potential for cancer therapy, and could significantly contribute to the planning of appropriate treatment and to increasing the patients' quality of life. The conventional therapeutic strategy is based on drugs that increase ROS generation and induce apoptosis in cancer cells. However, this therapeutic approach has serious disadvantages: the expression of various toxic side effects in normal (non-cancer) tissues. The current review describes the basics of free radical biology in carcinogenesis. The authors emphasize the different redox status of normal and cancer cells, which permits the use of this parameter as a new therapeutic target. The authors also outline some directions for the development of promising therapeutic strategies based on the regulation of redox signaling using combined therapy. The review is intended for a broad readership - from non-specialists to researchers in the field of cancer biochemistry and pharmacy.