Each of the pet friendly airlines has its own pet policy which could include holds, special pet carriers, required paperwork and more. Please read through each of the Pet Policy pages for the airlines you are considering. Hopefully, there will be a day when all pets can fly in the cabin. But until then, just make sure that you understand the policies for any airlines with which you plan to travel with your pet.
Below are links to most of the airlines traveling to and within the U.S. The Pet Policy pages are current.
Being an informed traveler is most important. This is why Pet Hotels of America has direct links to the Pet Policy pages of each of the pet friendly airlines.