The review summarizes physicochemical characteristics of the natural sesquiterpene peroxide artemisinin. The kinetic schemes of transformations of artemisinin radicals under anaerobic conditions are presented and analyzed. The sequence of radical reactions of artemisinin in the presence of oxygen is considered in detail. Special emphasis is given to the intramolecular chain oxidation resulting in the transformation of artemisinin into polyatomic hydroperoxide. The kinetic characteristics of elementary reaction steps involving alkyl, alkoxyl, and peroxyl radicals generated from artemisinin are discussed. The results of testing of artemisinin and its derivatives for the antimalarial activity and the scheme of the biochemical synthesis of artemisinin in nature are considered.