The story of the discovery of living polymers is presented. Living polymers are polymers that retain their ability to propagate and grow to a desired size while their degree of termination or chain transfer is still negligible. Theoretical and mechanistic considerations are discussed. The living polymerization technique provides access to uniform polymers (Poisson molecular weight distribution) of controllable size, block copolymers, functional polymers, and star and comb-shaped polymers. The quantitative aspects of electron transfer are fully discussed.