We all know how much little kittens love to have fun, and kittens will naturally scratch and bite as part of play and socialisation as they grow up. Their play fighting may involve some rough wrestling, however kittens will always interrupt this when if it becomes too much. If a kitten bites their littermate too hard, that kitten will cry to let the other know. This is important that kittens realise their boundaries, so they learn how to play appropriately.
Biting due to play aggression is more common in kittens or young adults that are the only cat in the household and thus have not learnt to inhibit their biting when playing with their siblings, and so we as owners become their unwilling victims!
Sometimes biting may be a fear response. If your kitten has not been well socialised or handled prior to adoption, they may be fearful of their new environment. It's important to take the time with these kitties to slowly get them used to being handled by patting them slowly several times a day and rewarding them with some treats to make this a positive experience. Feliway is a great addition to your home to help make your kitten feel more comfortable in their new surroundings. However if your kitten continues to be fearful, or suddenly starts biting or scratching when they previously didn't, please consult your veterinarian.