A block copolymer comprising: at least one monoalkenyl arene monomer polymer block (A) and copolymer block (B) containing myrcene, said copolymer block B also including: a) at least one conjugated diene monomer having a lower molecular weight than myrcene, or b) at least one monoalkenyl arene monomer, or c) a mixture of a) and b). The polymer block A may be a copolymer block. When the polymer block A is a copolymer block, both block A and the copolymer myrcene block copolymer B can have a random, tapered or a controlled distribution configuration of comonomers. The block copolymer can be selectively or exhaustively hydrogenated. The block copolymer may be used in making adhesives and vibration damping compositions.