Lycanthropes appear in many different cultures, more commonly known as werewolves, and they can only be killed by silver. In both myth and popular culture, there are many ways of becoming a werewolf, with the most well-known one (which is used in the series) being if an existing werewolf bites you.
In Greek mythology, Zeus invited Lycaon, the King of Arcadia, to dine with him. Lycaon wanted to know Zeus' real name. To prove that Zeus really was who he said he was, Lycaon tried to feed him human flesh. Then he hired assassins to attack Zeus while he slept to test the limits of his immortality. Zeus became so enraged he slew Lycaon's sons with lightning bolts and cursed Lycaon into being the first Lycanthrope.
Lycaon and his Lycanthrope minions await Jason Grace, Piper McLean, Leo Valdez, and Coach Hedge when they were on the search for Aeolus. He orders his minions to kidnap Jason, and kill Leo and Piper. They are later defeated when the Hunters of Artemis arrive. Lycaon is the only one to escape.
They later reappear under the command of Khione at the Wolf House. Since Lycaon was formerly injured by Thalia, he is not present; however his minions are there to fight for him. When Leo is fighting Khione he uses silver hammers to smash any wolves that got in his way. He and Jason kill all of them, but Porphyrion brings them all back to life when he awakes. The Lycanthropes were either all killed or scared off when Hera is freed and turns into her Divine Form.
The Lycanthropes are immune to weapons made of gold, bronze, and steel, as the weapon would just pass through them like mortals. The only thing that can kill them is silver. Despite silver being the only reliable way to kill a Lycanthrope, they can still be harmed in certain ways that will at least hold them back. Leo Valdez was able to hold them back with fire, but only for a short amount of time. Later, they appeared to be hurt by wood, though not fatally. They can also be hurt by lightning strikes, but it is unknown if it can hurt them to a fatal degree.