Vacationing with the dogs

I've taken my dog overseas with me. I do have a carrying bag that he can fit into and I slide him under the seat in front of me on airplanes. I just need to see what airlines allow pets in the cabin and see what type of restrictions they have. Some require vaccinations before entry and a full plane fare to have your dog in the cabin. Those are usually the last ones I chose to fly with. I hate spending money on a full adult human seat for a small dog that is sitting under the seat.