I'm also on the cat litter wagon. I use it in my garage to take care of the dog pee odors in the winter time when the dogs are too cold to go out into the yard to "go." Usually, the urine has already dried and the funk is just left over and it pulls the stink right out (as well as the stain). In cases where there is still moisture in the spot, it removes the moisture and the stink. I've tried the clumping kind and the cheap clay kind. The cheap clay kind actually worked better for me in the garage. The nice thing about it is I can then just toss it into the yard around the trees and work it into the soil. It will eventually decompose and become part of the soil (and keep the rabbits away from my bulbs when they bloom). It's not a ton of clay, so it's not inhibiting any growth and the soil around here is mostly clay anyway, so I don't think I'm hurting anything.
ETA: BTW: as an aside, cat litter is so strong at drying things out that it dehydrated the plastic container it was in. I had purchased a plastic container of clumping kitty litter as part of our Shelter In Place kit for work - you know, in case of an emergency when we're stuck in the vault and can't get out -- after three years of not needing it, we moved the container. When the agent picked it up, he got it in the air and moved it about two feet when the thing broke. He was holding the handle and the rest of it was all over the floor! The plastic container became so dry and brittle from the dehydrating nature of the kitty litter that it basically shattered under the weight of the clay. They made me clean it up because (1) I laughed way too loud at the whole thing and (2) the whole kitty litter and bucket was my "brilliant" idea. (I laughed way too much over that little piece of genius, too.)