Disclosed herein are 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. The non-natural amino acids, by themselves or as a part of a polypeptide, can include a wide range of possible functionalities, but typical have at least one oxime, carbonyl, dicarbonyl, and/or hydroxylamine group. Also disclosed herein are non-natural amino acid polypeptides that are further modified post-translationally, methods for effecting such modifications, and methods for purifying such polypeptides. Typically, the modified non-natural amino acid polypeptides include at least one oxime, carbonyl, dicarbonyl, and/or hydroxylamine group. Further disclosed are methods for using such non-natural amino acid polypeptides and modified non-natural amino acid polypeptides, including therapeutic, diagnostic, and other biotechnology uses.