Reptiles, also known as Class Reptilia, Class Sauropsida, or merely sauropsids, are ectothermic ("cold-blooded" -- though this term has now fallen out of fashion) animals covered in scales. There are over 8,200 reptile species, about 50% more than their relatives, the mammals. The reptile is one of the few taxonomic classifications among tetrapods that are polyphyletic -- meaning the group deviates from the convention of including all descendants of a common ancestor. Birds are actually descendants from ancient reptiles, the dinosaurs, but are not considered reptiles. If birds were included in Reptilia, the group would be monophyletic.
Reptiles are one of two amniote groups, the other being the synapsids, represented today by the mammals. Amniotes nurture their embryos using a series of complex membranes. By contrast, amphibians, that is, non-amniotes, have simple eggs that must be laid in water.
Reptiles and the ancestors of mammals, the synapsids, split from each other a very long time ago. The earliest known reptile, Hylonomus, and the earliest known synapsid, Archaeothyris both lived during the Late Carboniferous period, about 315 million years ago. They both superficially resembled small lizards, but gave rise to radically different descendants. Synapsids and sauropsids have since alternated in their domination of the Earth, with synapsids ruling from the Carboniferous until the Permian-Triassic extinction about 251 million years ago. From then on out, dinosaurs began to evolve, and the balance tipped back in favor of the reptile. That is why this period of time was called the Age of Reptiles. After the Cretaceous-Tertiary extinction 65 million years ago, all non-avian dinosaurs were obliterated, and synapsids, in the form of mammals, took over again.
There are four living Orders of reptile: Crocodilia (crocodiles, alligators, caimans, and gharials, 23 species), Sphenodontia (tuatara from New Zealand, 2 species), Squamata (lizards, snakes and amphisbaenids ("worm-lizards"), about 7,900 species) and Testudines (turtles and tortoises, about 300 species). The tuatara is considered a living relic, and is a popular subject of study among the phylogenetic and taxonomic communities.
The relationship between reptile groups can be confusing. Testudines either split off very early or is more closely related to the others: we don't know. Turtles lack holes in their skull, which is similar to some of the early reptiles, but they may have lost their skull holes more recently. Aside from Testudines, there are two main groups: archosaurs, which includes crocodilians and dinosaurs (including birds, which are descended from dinosaurs) and lepidosaurs, which includes everything else.