chain polymerization in which the kinetic-chain carriers are ions or ion pairs. It can be further divided into anionic polymerization and cationic polymerization. Ionic polymerization generates many polymers used in daily life, such as butyl rubber, polyisobutylene, polyphenylene, polyoxymethylene, polysiloxane, polyethylene oxide, high density polyethylene, isotactic polypropylene, butadiene rubber, etc. Living anionic polymerization was developed in the 1950s. The chain will remain active indefinitely unless the reaction is transferred or terminated deliberately, which allows the control of molar weight and dispersity (or polydispersity index, PDI). Coordination polymerization Coordination polymerization is a chain polymerization that involves the preliminary coordination of a monomer molecule with a chain carrier. The monomer is first coordinated with the transition metal active center, and then the activated monomer is inserted into the transition metal-carbon bond for chain growth. In some cases, coordination polymerization is also called insertion polymerization or complexing polymerization. Advanced coordination polymerizations can control the tacticity, molecular weight and PDI of the polymer effectively. In addition, the racemic mixture of the chiral metallocene can be separated into its enantiomers. The oligomerization reaction produces an optically active branched olefin using an optically active catalyst. Living polymerization Living polymerization was first described by Michael Szwarc in 1956. It is defined as a chain polymerization from which chain transfer and chain termination are absent. In the absence of chain-transfer and chain termination, the monomer in the system is consumed and the polymerization stops but the polymer chain remains active. If new monomer is added, the polymerization can proceed. Due to the low PDI and predictable molecular weight, living polymerization is at the forefront of polymer research. It can be further divided into living free radical polymerization, living ionic polymerization and living ring-opening metathesis polymerization, etc. Ring-opening polymerization Ring-opening polymerization is defined as a polymerization in which a cyclic monomer yields a monomeric unit which is acyclic or contains fewer cycles than the monomer. Generally, the ring-opening polymerization is carried out under mild conditions, and the by-product is less than in the polycondensation reaction. A high molecular weight polymer is easily obtained. Common ring-opening polymerization products includes polypropylene oxide, polytetrahydrofuran, polyepichlorohydrin, polyoxymethylene, polycaprolactam and polysiloxane. Reversible-deactivation polymerization Reversible-deactivation polymerization is defined as a chain polymerization propagated by chain carriers that are deactivated reversibly, bringing them into one or more active-dormant equilibria. An example of a reversible-deactivation polymerization is group-transfer polymerization. Comparison with step-growth polymerization Polymers were first classified