Non-natural amino acids and polypeptides that include at least one non-natural amino acid, and methods for making such non-natural amino acids and polypeptides, are disclosed. The non-natural amino acids, by themselves or as a part of a polypeptide, can include at least one oxime, carbonyl, dicarbonyl, and/or hydroxylamine group. Methods for making, modifying, and purifying the non-natural amino acid polypeptides are also disclosed. Further, methods for using such non-natural amino acid polypeptides and modified non-natural amino acid polypeptides, including therapeutic, diagnostic, and other biotechnology uses, are disclosed.