The control achievable by living radical polymerization (LRP) is based on a kinetic balance of the activation-deactivation reversible reactions, which are specific to LRP, with conventional elementary reactions such as initiation. propagation, and termination. This work describes, as plainly as possible, how chains grow and how their polydispersity evolves as they experience activation-deactivation cycles and how these processes can be quantitatively analyzed by gel permeation chromatography. A comprehensive probability theory on the polydispersity indices of LRP polymers is presented. (C) 2004 Wiley Periodicals, Inc.