Styx

"For thousands of years, you humans have been throwing in everything as you come across—hopes, dreams, wishes that never came true. Irresponsible waste management, if you ask me."

- Charon

The River Styx (meaning "hate" and "detestation") is a special river located in the Underworld. This is the actual river that separates the land of the living from the realm of the dead.

History
Styx was a nymph that, due to her effort in the first Titan war, gained a very important role in Greek mythology. by me

Description
The river was a sacred place to both gods and men. It circles the Underworld nine times, eventually converging on a great marsh at the center of the Underworld with the rivers Phlegethon, Acheron, and Cocytus (though there is a fourth river: Lethe). According to Percy, the river is very polluted, being filled with pretty much anything you could imagine: broken toys, ripped up diplomas, etc.–the scrapheap of human miseries. The river is filled with lost hopes and dreams, as well as wishes that never came true. The River Styx is also where Stygian iron is cooled to make it indestructible, as well as where Stygian ice is formed. Heroes who bathe in it become invulnerable (only Achilles, Luke Castellan, and Percy Jackson have successfully done this though). As well, Styx was a goddess - similar to the rivers Phlegethon, Acheron, and Lethe being associated with deities and a daughter of Oceanus and Tethys. She was the wife of Pallas and bore him Zeus' four winged enforcers: Kratos, Nike, Zelus, and Bia (and sometimes Eros). Styx supported Zeus in the Titanomachy, being the first to aid Zeus in the First Titan War against Kronos and his Titan Army. For this, her name was honored by being used in binding oaths.

Swearing on the River Styx
The River Styx is also part of a powerful oath that can be made between any group of people. Breaking an oath on the Styx is extremely unwise for anyone due to the fact that once you swear upon it, the Fates are now watching. Gods who break oaths on the Styx apparently "get off lightly" on the account of being immortal such as when Zeus and Poseidon broke the oath of having no more demigod children after the disastrous end of World War II. It is unknown what would happen if a lesser entity were to break an oath on the Styx, but it is considered unpleasant. According to the myths the books are based on, the consequences for breaking an oath made upon it are supposed to be extreme. The oath-breaker is supposed to be exiled from the assembly of gods for ten years and be denied nectar or ambrosia during this time. The first year they lie in a coma like state unable to move in any way. The rest they are denied attending any of the assemblies or festivals of the gods for nine years. Despite this, both Zeus and Poseidon avoided this. Since Zeus is in charge of enforcing oaths there was no one to force him to go into exile. His importance in the council and the fact that he maintains order on Mount Olympus probably had something to do with it as well. This was probably brought about by his great arrogance and general dislike for following his own rules. Poseidon's status and power no doubt protected him as well making exiling him too difficult. Ironically, Hades is the only one of the Big Three that can be trusted to keep his word when there are no direct consequences. In The Son of Neptune, Percy asks Hazel if, because Death is chained, an oath on the River Styx is still binding and she says it is.

Oaths

 * Annabeth Chase, swore to Chiron that she would try her best to protect Percy. (The Sea of Monsters)
 * Bianca di Angelo, to serve Artemis and always be a maiden. (The Titan's Curse)
 * Antaeus swore on Percy's terms to allow him and his companions through the arena had Percy defeat Antaeus. (Battle of the Labyrinth)
 * The Big Three, to never have demigod children again. (Oath no longer in effect after The Last Olympian)
 * Zeus, on behalf of the council to grant Percy's reasonable request, linking on to following point. (The Last Olympian)
 * The Olympians, to claim all their children by the age of thirteen and give the other gods cabins. (The Last Olympian)
 * Nico di Angelo, that he didn't know what Hades planned. (The Last Olympian)
 * Annabeth to Jason Grace, promising not to reveal his secret until Jason had more information or allowed her to. (The Lost Hero)
 * During The Son of Neptune, Percy made several promises all under one promise on the River Styx when trying to gain information from Phineas, including:
 * Percy promised that the two vials of Gorgon Blood were identical and he didn't know which one healed and which killed.and that he didn't know which one would heal or which one would poison.
 * Percy and Phineas promised to drink the vials at the same time.
 * That if Percy won, the harpies would be free of their curse. However if Percy won, Phineas would be forced to tell them the location of Thanatos, and by extension, Alyconeus' layer.
 * If Percy lost, Hazel Levesque and Frank Zhang wouldn't seek revenge against Phineas.

Achilles' Curse
Anyone who bathes in the River Styx will be gifted with the strength, power, speed, and near invincibility of Achilles. The only spot where one who has bathed in the River Styx is vulnerable is in their Achilles Heel, a spot of the bather's choosing which will keep them grounded to the real world and their mortal life after they bathe in the river. If the person doesn't focus on that point while bathing in the river, their soul will be incinerated, washed away in the current. Achilles' ghost appears to anyone who wishes to receive the curse, warning them not to. The ghost claims it will affect them highly, but it shows few signs in Percy.

Bearers of the Curse
There have only been three people to have bathed in the river so far and lived:
 * Achilles - His mother dipped him into the river by his heel early on in his life when he was only a baby boy years before the Trojan War. Therefore, his heel is vulnerable. He was killed in the Trojan War by an arrow from Paris that struck him in his heel.
 * Luke Castellan - Luke bathed in the river so that his body could become invincible, giving his body the ability to hold Kronos' spirit. His Achilles spot is under his left arm. He possibly envisioned himself and Thalia first meeting and starting a romantic relationship and giving his knife to Annabeth Chase. He stabbed himself to destroy Kronos before he could take on his own form and died by his own hand to end the Second Olympian War.
 * Percy Jackson - Nico di Angelo suggested to Percy that he should dip himself in the River Styx so that he could defeat the Titan Lord Kronos in the Battle of Manhattan. Percy was first uncertain about this idea but eventually decided to go through with it. His Achilles' Heel was the small of his back, opposite of the navel. He pictured it like the time when he fell out of the boat and was being pulled out of the water by Annabeth. He later lost the blessing after touching the Little Tiber when entering Camp Jupiter, because it is a Greek blessing.

Trivia

 * The River Styx is the only body of water that Percy can't breathe in.
 * Like the rest of the Underworld rivers, the Styx is an immortal nymph, but does not take an actual form.
 * In The Demigod Diaries, Leo Valdez mentions that part of the fuel for the Argo II is water from the River Styx.