There are no restrictions on the kinds of animals that you can describe as emotional support animals. But now, United Airlines has joined Delta in restricting people from taking any old pet on planes under that classification.
This review comes on the tail of a recent, bizarre controversy where an artist tried to bring her "emotional support peacock" on board a United flight, and the airline denied her.
The peacock was apparently the last straw, but the new rules have been under consideration for a long time. In 2017, passengers flying United Airlines declared 76,000 animals as "emotional support animals," up from 43,000 in 2016, a United spokesperson told USA Today.

Previously, United only required 48 hours advance notice and a note from a medical professional stating that the animal has to accompany their owner. Now, passengers have to provide more documents, including a statement from a vet saying that the animal is trained to behave in public settings and is healthy.
The new rules will come into effect on March 1, 2018, on the same day that Delta will start enforcing similar rules. That airline also experienced a surge in people bringing animals on board and claiming them as service animals. Perhaps most famously, in 2000, US Airways kicked an "emotional support pig" off a flight because it was 300 pounds and defecating on the plane.
That doesn't mean that people can't take animals on a plane. You can ship them via cargo, but you still need documentation to do that, and it's risky. You can also bring pets in the cabin with you if they are a dog, cat or bird small enough to fit in a carrier that can go under the seat in front of you. On United Airlines, that's 17 inches by 10.5 by 20. So, good luck fitting your pig, peacock or golden retriever there.
On the other hand, real service animals and trained emotional support animals can be out of a crate and on the lap of their owner in-flight. There is less of a concern about the animal becoming distressed and acting out if they are trained to handle public situations.
Keep in mind, however, that there is no national registry of emotional support animals, as Cathy Zemaitis, director of development for National Education for Assistance Dog Services (NEADS), in Princeton, Massachusets, told WebMD, "A big red light should go off the minute someone says their service dog is registered."