Children of the Moon are creatures most similar to the traditional werewolves of myth.
They phase, or change form, in response to the cycles of the moon. In their changed form, they do not entirely resemble actual wolves: their forelegs are more powerful than their hind legs, and they still have usable hands with opposable thumbs. In addition, their stance is more upright, making their movement somewhat apelike, rather than entirely canine.
Children of the Moon change form only at night, and during the fullest phase of the moon. While in their werewolf form, Children of the Moon are not aware of their human selves; they are feral rather than rational. Usually, they run alone, or with one companion of the opposite gender. Children of the Moon cannot breed in their animal form; they can spread their species only by infecting other humans through a bite. Infected humans who have children do not pass their abilities to their offspring.
In their animal form, Children of the Moon have heightened strength and speed that make them both deadly and difficult to kill; contrary to legend, these werewolves cannot be killed with a silver bullet, nor does silver repel them. Their amplified abilities make them capable of destroying a lone vampire. One advantage the werewolf has in both his/her human and animal forms is immunity to vampire venom, both the transformative properties and the pain-producing properties.
Because vampires and Children of the Moon share the same food source and because each is an exception to the other's near indestructibility, they are natural enemies. Over time, however, the vampires have hunted the once populous werewolves into near extinction.
Not much is known about the Children of the Moon. It is known that Caius, one of the Volturi leaders, is terrified by them after he was nearly killed in a fight with one two thousand years ago. Aro and Marcus knew about Caius' encounter, and since werewolves pose a threat to vampires everywhere, they initiated a war against them, resulting in the near extinction of the werewolves in Europe and Asia. It is not known if they are found anywhere else in the world. In Eclipse, it also stated that James hunted one across Siberia though unaware of what it was.
The Volturi refuse to tolerate truces or alliances between werewolves and vampires, under likely punishment of death. This was something that Caius tried to stress when the Volturi put the Cullen family on 'trial' for creating an immortal child. But the werewolves the Cullens had allied with were really shape-shifters in wolf forms, and the law didn't apply.
Due to the Volturi's initial assumption that the La Push shape-shifters were Children of the Moon, the two groups probably look very similar in their wolf form.
Children of the Moon rarely form packs. It is not known if they show social characteristics similar to the Quileutes, such as hierarchy. However, in Breaking Dawn, it was commented that true werewolves are disorganized compared to the shape-shifters. They only run with one companion of opposite gender.
It has been confirmed that they cannot breed in animal form. Like vampires, they change people into werewolves by biting them, infecting them with their poison. However, they do not pass this infection to their offspring. Unlike the legendary version they're based on, they are not vulnerable to silver bullets.
Werewolves do not age, show flowing blood and a beating heart like humans, and they smell unappetizing to vampires. Werewolves consume flesh, human or animal. Like shape-shifters, werewolves probably have enhanced strength and speed, rapid healing, and heightened senses. They may or may not possess gifts. Also they are immune to vampire venom in both human and animal incarnations.