Titan's Curse
The Titan's Curse is the burden of holding up the sky to prevent its weight from crashing down upon the earth. The curse can only be forced upon a @Titan, though a pure-hearted hero can willingly take on the burden if they choose to, as can gods. It can give excruciating pain.
Background
After the @Olympians' assault on @Mount Othrys, @Zeus confined his four Titan uncles to @Tartarus as punishment. Laughing at the gods' ignorance, @Atlas reveals that the presence of the four Titan Lords is the only thing keeping the sky in place. As a solution to this problem, Zeus had the Elder Cyclopes chain Atlas to a mountain and cause the sky to form a central support pillar, which they then forced upon his shoulders to bear as punishment.
As his tenth labor, @Hercules had to obtain the golden apples of immortality from the Garden of the Hesperides. Unable to bypass @Ladon, Hercules was instructed by Atlas' daughter, Zoë Nightshade, to trick her father into stealing the apples for him. Hercules did so by taking on the Titan's Curse while Atlas obtained the apples for him, but upon returning, Hercules once again tricked the Titan into taking on his burden once again.
Second Titan War
@Luke Castellan takes on the Titan's Curse to free Atlas from his punishment. While on a mission to retrieve two half-bloods from @Westover Hall, @Annabeth Chase is kidnapped by the @Manticore and tricked by Luke into taking the burden of the sky from him. When @Artemis herself is captured by Atlas while hunting the @Ophiotaurus, she willingly takes the burden from Annabeth, who was on the brink of dying from holding up the sky too long.
The Oracle issues a quest to Zoë so they can free Artemis. She takes @Thalia Grace, @Grover Underwood, and Bianca di Angelo as companions, with @Percy Jackson later joining them. Bianca dies during the quest but the others reach their destination, the ruins of Mount Othrys. A battle ensues, in which Percy frees Artemis and convinces her to let him bear the Titan's Curse, thus fulfilling the Oracle's prophecy in doing so. In the midst of battling Atlas, Artemis once again forces the burden of the sky onto the Titan General, relieving Percy of it at the same time. @Poseidon later confirms that no one from the Titan Army would be willing to hold up the sky for Atlas. However, Percy realizes that Luke decided to take on the burden, albeit only to trick Annabeth.
A year later, in a dream, Percy sees Atlas still trapped under his burden. He demands that @Krios and @Hyperion let him out, as he is the Titans' greatest warrior. Hyperion reminds Atlas that he failed when he was freed from his burden, and that he is better suited to remain where is, holding up the sky.