This chapter demonstrates how the kinetics of an ideal living polymerization leads to a narrow, Poisson distribution of chain lengths. It considers chain-growth polymerization via an anionic propagating center; this has historically been the most commonly used controlled polymerization mechanism, and it can be conducted in such a way as to approach the ideal case very closely. The chapter explores how the anionic mechanism can be extended to the preparation of block copolymers, end-functional polymers, and regular branched polymers of various architectures. It also explores the other mechanisms that are capable of controlled polymerization, including cationic, ring-opening, and, especially, controlled radical polymerizations. One common feature that emerged from the discussion of these mechanisms is the statistical nature of the polymerization process, which led directly to rather broad distributions of molecular weight. The chapter concludes by addressing the concept of equilibrium polymerization and a special class of controlled polymers called dendrimers.