Compositions, kits, and methods for repairing bonds, for example, disulfide bonds, in hair or on the skin are disclosed. The compositions provide improved conditioning benefit for dry hair or moisturize the skin. The compositions also provide a long lasting moisturized feel and smooth feel to the skin or hair, without feeling greasy. The compositions contain one or more compounds that covalently crosslink at least two thiol groups in the hair or on the skin. Use of the crosslinking compositions prevents reversion of the repaired bonds to their reduced (thiol) state, for at least one week, one month, six months, or one year, after a single application of the composition. Improved methods of styling hair, for example permanent hair waving, hair curling, and hair straightening are also provided.