Polymers containing amino acid and/or polypeptide moieties in their backbones or pendant to their backbones are made by metathesis. A method of making an amino acid or polypeptide containing polymer includes the steps of: providing a amino acid, amino alcohol, or polypeptide-containing monomer; forming a reaction mixture by contacting the monomer with an agent capable of catalyzing the polymerization of the monomer into a polymer; and placing the reaction mixture under conditions that result in the formation of the polymer in reaction mixture.