Our waste hauler specifically says not to put cooking oil in the compost bin. I save it in the bottles it comes in and put it in the regular trash, where is likely goes to a landfill, as @KennethT said.
There are oil and grease recyclers that accept used cooking oil. Last time I checked, there wasn't one handy to me but should check again.
Edited to add that there are plenty of places that accept used motor oil. I suppose because any place that sells it is required to accept it for recycling. Too bad the grocery stores don't have the same mandate to collect used cooking oil.
