Also your pet levels with you, growing in power and hitpoints as you level (though it takes MUCH less for it to level than you).
Say you get a 20th lvl pet at 20th lvl. Now though it only takes 6800 xp for pet to level, it takes you like 30,000 (just for arguments sake, not sure on the number). Your pet will NEVER out lvl you, if you are both 20th lvl, you pet will get no more xp till you lvl to 21st, then it will start to accure xp and usually by the time you are 1/4 the way into 21st the pet will ding 21st.
This is so that if you are 20th lvl and tame a 15th lvl pet, it will catch up to you in levels before you ding 21.
You can have multiple pets, but be in command of only one at a time.
I have a bear pet and a raptor pet. I keep the raptor at the stables unless I want a damage dealing pet, the bear is better in terms of HP and AC, but does less damage. So if I want the raptor, I go to a stable master, swap pets and off I go.