Thermoplastic vulcanizates comprise at least an ethylene/.alpha.-olefin interpolymer and at least one thermoplastic polymer, such as polyolefin. The ethylene/.alpha.-olefin interpolymer is a block copolymer having at least a hard block and at least a soft block. The soft block comprises a higher amount of comonomers than the hard block. The block interpolymer has a number of unique characteristics disclosed here. The block interpolymer is either used as a compatibilizer between a vulcanizable elastomer and a thermoplastic polymer or as a vulcanizable elastomer when it is in the EPDM form. The thermoplastic vulcanizates can be profiled extruded to make profiles and gaskets.