New thermoplastic elastomers are produced by living radical polymerization and living carbocationic polymerization. SIBS is produced by living carbocationic block copolymerization of isobutylene monomer and styrene. SIBS has superior gas barrier, thermal stability and energy absorption capability. Styrene content, molecular weight and hardness are influence the mechanical properties of SIBS. The melt viscosity of SIBS is lower than other TPSs and SIBS is also softer without added oils than other TPSs. The product is utilized in the applications such as hot melt PSA, adhasives, dampening components etc. Thermoplastic elastomers based on acrylic block copolymer is prepared by atom transfer radical polymerization which is one of the living radical polymerization.