Dogs on Airplanes?

So, every time I go to the airport, I always see, without fail, larger dogs trotting around! All sizes from pretty small to very tall and large like a 50+ pound dog. I don’t understand because every single airlines I’ve checked (well, from the main airlines) say your dog needs to fit in a small carrier and fit under the seat in front of you. How are all these people bringing their larger dogs? I always tell myself I’ll just ask the next owner I see of a larger dog in an airport, but I sort of chicken out. I have a beagle, he’s like 30 pounds and not that big but just kinda misses the requirements to fit in a carrier small enough to fit in the seat in front of me… so how are these people doing it?! If you’ve ever brought your larger than 20 pound dog on an airplane please let me know how!!!