This paper will discuss the design and synthesis of polyisobutylene-based thermoplastic elastomers (TPEs) for biomedical and other specialty applications. The first generation from this class of polymers, linear triblock polystyrene-b-polyisobutylene-b-polystyrene (PSt-b-PIB-b-PSt or SIBS), is FDA-approved and currently used as the polymeric coating on drug-eluting coronary stents. TPEs with arborescent (dendritic) polyisobutylene core (arbPIB-b-PSt) the third generation, display unique combination of properties. Our latest results include the synthesis of surface-modified TPEs. This paper will give a short overview of the effect of architecture (number of branches, molecular weight and size) on select properties of arbPIB-based TPEs. It will be demonstrated that block copolymers with a high molecular weight dendritic (arborescent) polyisobutylene core and poly(para-methylstyrene) end blocks can manifest themselves either as a rubber, or as a plastic, depending on their environment. The behavior is thermally irreversible. We called this material the “chameleon thermoplastic elastomer.” This material represents a new concept in material science: ETPE (entropy-driven thermoplastic elastomer).