Semi-crystalline, thermoplastic polyolefin block copolymers comprising: (A) A first polyolefin A block comprising isotactic poly(1-butene) (iPB); (B) A polyolefin B block comprising an ethylene and/or alpha-olefin/1-butene copolymer or terpolymer; and (C) A second polyolefin A block comprising isotactic poly(1-butene) (iPB); the A and B blocks bonded to one another to form a block copolymer in which the first and second polyolefin A blocks are joined to and separated by the polyolefin B block. In one embodiment the polyolefin block copolymer is a BAB block copolymer.