Two phrases do most of the work on a skincare front of pack, and neither means what a shopper reads into it. If you read one thing in this section, read what clinically proven is allowed to mean: the phrase has no fixed definition in cosmetics, and what sits behind it is usually a study designed to support a wording rather than to test a product. Then read the difference between dermatologist recommended and dermatologist tested, which are not the same claim and do not require the same evidence.
The rest of the section is the machinery behind both. A claim has to be held up by a documented evidence file before it is printed, which is how a claim is substantiated; three of the words that appear most often on packs have no agreed legal definition at all, which is how natural, clean and free from claims work; and when a claim is challenged the process is public, which is what the ASA actually does.
None of that answers the question a reader is usually asking, which is whether a particular product is going to suit their own skin. No claim on a pack can answer it either, because a claim is held up by evidence about people in general rather than about you. The one test that is about you is the one you run yourself, and how to patch test a cosmetic product at home sets out how to do it, what a negative result does and does not license, and when not to test a product at all.
