The Hijacking and Retaking of the Iliad was the height of the War Against the Inhumans, when the Inhuman supremacist leader Jiaying attempted to take over the S.H.I.E.L.D. aircraft carrier Iliad to spread Terrigen Mist over the world.
The result was a firefight amongst the S.H.I.E.L.D. agents on board the carrier, led by Phil Coulson and Anne Weaver, and Jiaying's Inhumans from Afterlife. Although S.H.I.E.L.D. prevailed and the surviving Afterlife Inhumans surrendered after Jiaying was killed, a case of impure Terrigen Crystals had successfully dispersed over the Atlantic Ocean in a crashed Quinjet, triggering an international outbreak in the Inhuman population.
The Inhumans, created by the Kree to be used as weapons, founded a settlement named Afterlife to keep themselves separate from normal humans. Occasionally the Inhumans would come into contact with humans, with mostly bad results.
Jiaying was experimented on by Daniel Whitehall, who discovered her longevity and wanted it for himself. He vivisected Jiaying, supposedly killing her, before disposing of her body in a ditch. Unknown to him, Jiaying was discovered by her husband, who stitched her back up and allowed her powers to heal her. However, the trauma changed Jiaying from a compassionate person to a person consumed with hatred for humans. 
Through encounters with Vin-Tak, Gordon and Raina, S.H.I.E.L.D. discovered the existence of Afterlife and insisted on meeting the leader of the settlement. Jiaying agreed to meet S.H.I.E.L.D., forming a plan to destroy humans and build a better world for Inhumans.
When Robert Gonzales arrived at the Afterlife, Jiaying killed him and made it seem as if he had tried to kill her. The Inhumans followed her lead and began preparing for war, while S.H.I.E.L.D. returned to their base to regroup. Jiaying formed a plan to attack the Iliad and release Terrigen Mist over the world. 
Gordon, Alisha Whitley, Lincoln Campbell, and other Inhumans teleported onto the Iliad. They quickly took over the entire ship and took the crew as hostages. Once the ship was under Inhuman control, Jiaying boarded the ship with cases of synthetic Terrigen Crystals. Campbell warned Jiaying of an emergency beacon sent out from the ship, and Jiaying ordered Oliver to expand it; when he refused, she locked him and other agents in a room and broke a Crystal inside, petrifying them. She then ordered Anne Weaver to expand the beacon, which she did.
Skye was imprisoned on the Iliad, having confronted her mother over her plan. Alphonso Mackenzie found and freed her, leaving to find equipment while she reset the emergency beacon. Skye set the beacon to warn S.H.I.E.L.D. away but was found by Lincoln Campbell, who blasted Skye before she was able to start convincing him of Jiaying's true intentions. Just as Campbell started to listen to Skye, he was knocked out by Mackenzie, who then left to guard the Crystals.
At the Playground, Phil Coulson received the emergency signal and set out with Leo Fitz, Calvin Zabo, and other agents. When Skye's message warning of the trap was received, Coulson ordered the other Quinjets to fall back while he continued. Arriving at the ship, Fitz and Coulson went to help Mackenzie while Zabo went to confront his wife, only to be imprisoned.
Gordon entered the room with the Terrigen Crystals, and Mackenzie challenged him. The two fought each other until the arrival of Coulson and Fitz. Immediately, Fitz set up Quantum Field Disruptors, which trapped Gordon inside the room. The three agents continued to fight Gordon until he accidentally teleported himself onto an iron pole that Fitz was holding. As he fell, Gordon released a Crystal he had been holding; Coulson dove to catch it and his arm started to petrify. Just as the petrification reached the elbow, Mackenzie chopped Coulson's arm off, stopping the petrification and saving Coulson's life.
Skye was attacked by Alisha Whitley, who made duplicates of herself in the fight. Skye was nearly defeated when Melinda May and Campbell arrived to assist her. Skye left to find Jiaying while May and Campbell continued fighting Alisha. Campbell electrocuted the prime Alisha and her duplicates passed out.
Jiaying went to the deck of the Iliad, where a Quinjet was being loaded with Terrigen Crystals. As she was watching her men, she was confronted again by Skye. Jiaying tried to convince Skye one more time that she was right, but when Skye refused to help her, Jiaying began using her powers of life absorption to kill her daughter. However, Skye mustered her energy and blasted the Quinjet, with the Crystals inside, into the ocean. Angered at the destruction of her plan, Jiaying again tried to kill Skye, only to have Skye use her powers to try to kill her. Eventually, Calvin Zabo, who had escaped his cell, found the two women and separated them. Zabo broke Jiaying's spine, killing her and saving Skye.
The artificial Terrigen Crystals dissolved in the ocean water and intermingled with the ecosystem. The sea life ingested the chemicals, were eventually caught by fishermen, and turned into Nature Max Supplements Fish Oil pills that were distributed worldwide. Phil Coulson decided to begin a new program, similar to the Avengers Initiative, where superpowered individuals were to be found and trained. Skye was the first recruit. According to Alphonso Mackenzie, the battle that was on the Iliad took many S.H.I.E.L.D. agents months to recover.