Puppies explore with their mouths because they have no hands. Mouthing is also how they play with other puppies, and they learn how hard is too hard from that play. Welfare groups such as the RSPCA and SSPCA describe play biting as normal puppy behaviour, not aggression. It still hurts, and it needs teaching, because a bite that is gentle at 10 weeks is not gentle at 10 months.
Biting that comes with stiff body language, growling over food or toys, or a puppy that looks scared is a different thing. That is not play, and it will not fade on its own. Ask your vet for a referral to a qualified, reward-based behaviourist.
Pick what is happening and your puppy's age. The plan shows what to do instead, using only rewards and calm breaks.
What is the puppy doing?
When teeth land on skin, the game stops for a short, calm moment, then restarts with a toy. That is all. It teaches "teeth on people means fun ends; teeth on toys means fun continues". Keep it boring: no shouting, no pushing the puppy away, no holding the muzzle shut. Welfare groups warn that punishment can make a puppy fearful and often makes things worse. Even saying "no!" can count as attention that rewards the nipping.
Teach what to bite, not just what not to bite: reward the toy every time.
Most puppies get better with steady, kind practice over weeks. Teething makes chewing stronger for a while: Blue Cross describes teething as roughly 3 to 7 months, with another burst of chewing in adolescence, and PDSA says baby teeth start to be replaced at around four months. Sources differ a little on exact ages, because puppies differ. If you see very wobbly adult teeth, bleeding gums or your puppy stops eating, ask your vet.