Flavonoids represent a structurally rich group of plant metabolites with a large variability of biological activities beneficial to human health. Their proven antioxidant and anti-inflammatory properties correlate with antitumor activity, because their common denominator is oxidative stress. Research into the mechanisms of the antitumor effects of natural substances is particularly topical. The use of natural products as chemotherapeutic drugs would help solve the problems of resistance to currently used synthetic chemotherapeutics and their side effects. In this work, we briefly summarize the causes of carcinogenesis, mechanisms of apoptosis, oxidative stress and the consequences of oxidative damage, as well as the importance of maintaining redox homeostasis and pro-oxidative conditions for cells. DNA damage by chelates of redox-active metal ions with flavonoids under in vitro conditions is also discussed as a potential mechanism for induction of apoptosis. The present work provides information on the structure, occurrence and bioavailability of flavonoids quercetin, apigenin and genistein and an overview of some molecular mechanisms of their antitumor action, including interference with apoptotic pathways.