Some cats are teenagers ALL their lives
But usually the most active, getting into mischief, etc. is between 6 months and 2-3 yrs old. Some start to slow down after a few years; others will still race around the house over 10 yrs old.
And some breeds are a lot more active longer - such as abys, siamese, rexes, ocicats; compared to a persian/himalayan type.
As far as kitten age - technically 8 months is considered an adult cat for show purposes, so I go by that rule rather then the 1 year old being an adult.