Chain growth polymerization involves monomers adding together in a chain reaction to form long polymer molecules. There are three main types: free radical, cationic, and anionic polymerization. Free radical polymerization is initiated by molecules like peroxides that generate free radicals to start the chain growth. It proceeds in three steps - initiation, propagation where monomers add to the growing chain, and termination when the reaction ends. Cationic polymerization uses acids as initiators and transfers a cation to the monomer. Anionic polymerization uses bases as initiators and transfers an anion to start the chain growth. Common products include polystyrene, polyisobutylene, and elastomers.