An ATC is a tube-style rappel device. The ATC has two slots for up to two ropes. A bight of rope goes through the slot then a carabiner is clipped through the rope. The steel cable doesn't look very strong, and it isn't. It's only there to clip to so you don't drop the ATC, not for supporting your weight. To lock off an ATC, thread the brake strand through your locking carabiner and up the other side then tie a mule hitch.
The ATC is easy to attach and inspect. It works with single strand (a good amount of friction) or double strand (a lot friction). ATCs are relatively cheap. I bought mine for $10 in 2010.
An ATC can get really hot on long rappels. It shouldn't do any damage to your rope, but it can really hurt your fingers.
ATCs are complicated to lock off.
I have found it difficult to thread my 11mm static rope through my ATC when my fingers are numb from the cold.