If cats do not have enough activity or mental stimulation throughout the day they will become destructive in the home. This may be, but is not limited to: damaging/scratching furniture, wallpaper, breaking ornaments/possessions, toileting all over the house, aggression, hyperactivity.
Kittens will display a lot of these behaviours as they are growing so you must be prepared to kitten-proof your home and ensure that they cannot knock off items and damage as little as possible. You should expect some form of destruction to occur in the home.