What is a bird?
Two-legged, bipedal vertebrates, distinguished from other living vertebrates by feathers. All birds have bills, and they have a 4-chambered heart.
~ after Gill, F. B. 1995. Ornithology
Second edition. Freeman, New York
Kingdom: Animalia (animals)
Phylum: Chordata (animals with a spinal chord)
Subphylum: Vertebrata (animals with a backbone)
Class: Aves (living and extinct birds)
Living: crocodiles & alligators
Extinct: theropod dinosaurs (probably) or crocodilians and dinosaurs together (alternative hypothesis, which envisions a common ancestor for birds, crocodilians, and dinosaurs, probably in the late Permian or early Triassic Period)
We now know that some dinosaurs had feathers, as explained at these sites:
National Geographic Society
Australian Museum online