Some exfoliators can irritate skin. If you're concerned about this, ask for samples. They're more likely to be available for the higher-end exfoliators than those sold in drugstores. Call a company directly if you can't get a freebie at the store. Test it for a few days by applying a dab on your temple before you use it all over your face.
Highest concentrations are comparable to retinol.
Salicylic acid and related chemicals that work like AHAs but are slightly less effective. Mildly abrasive pastes that mechanically remove dead cells on skin's surface. Someone who likes the just-scrubbed feeling. Clay, mud, or other peel-away preparations that are very light exfoliators. Skin that needs more oil control than exfoliation.