Yes — Delta Air Lines does allow pets, but with specific rules. Small dogs, cats, and household birds can travel in the cabin if they fit in an approved carrier under the seat and you pay the pet-fee at check-in. Pets cannot travel as checked baggage in the hold; instead, larger animals must go via cargo (except for certain military/State-Dept exceptions). Also, there are many destination, age, breed and kennel-size restrictions (e.g., pets to/from many international locations are not allowed in the cabin).
