range hood, vent for stove

Can a range hood vent go out the side of the house to the outdoors, or do they have to go through the roof?
I was thinking if I could just run it right out through the back of the wall it would be outside right there, and probably be a shorter run that way. Plus it would be one less thing to worry about leaking or keeping up on my roof since the roof will be metal. Right now I have a range hood with the charcoal filter that just pulls air up and then spits it back out the top into the room. I don't like it at all, it isn't efficient. I hate laying in bed at night and can still smell whatever I cooked for dinner hours ago....