Two examples of asymmetric alternating copolymerization, (1) the alternating copolymerization of alpha-olefins (monosubstituted ethenes) with carbon monoxide and (2) the alternating copolymerization of meso-epoxide with carbon dioxide, are described, and the meaning of chirality in polymer synthesis is emphasized. (C) 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 215-221, 2004.