The possibility of the synthesis of well-defined polymers by radical polymerization is discussed. Kinetic analysis demonstrates that the preparation of polymers with controlled macromolecular structure in a "living" radical process requires a low stationary concentration of growing radicals which are in a dynamic equilibrium with the dormant species. Three approaches are described : first, when growing radicals react reversibly with scavenging radicals to form covalent species, second, when growing radicals participate in the degenerative transfer reaction which regenerates the same type of radicals. Some of the reported "living" radical systems are critically evaluated.