The third of the Vishantis, Agamotto, created three eyes, one of Power, one of Truth and of Prescience. This artifact is actually the third of Agamotto's "eyes", but is the one most commonly associated with the term.
It is the name commonly given to Doctor Strange's amulet, though the Eye actually resides within the amulet and is released from time to time. The Eye itself gets its name from Agamotto, a powerful mystic being who used it during his time as Sorcerer Supreme of the Earth dimension. It first appeared in Strange Tales #115.
The Eye traditionally belongs to the Earth dimension's main opponent to Dormammu, a sinister mystical being. After he defeated Dormammu for the first time, the Eye of Agamotto came into the possession of Doctor Strange. The Ancient One was given to repel Dormammu and other mystic threats to the Marvel Universe, and apparently Margali Szardos, who knew of the Eye and told Strange that he was not the first custodian of the ancient amulet, she tells him he will not be the last either, magically summoning the Eye by a gesture of her hand, and Strange is shocked, as he could not even prevent the eye from going up to Margali and wonders who this woman is. Margali says a chant relating to the Eye, and a golden glow shines down on Kurt, it is the Eye of Truth. 
The Eye of Agamotto set off the metal detector at the airport, which the Sorcerer Supreme detested, indicating the Eye is made of some metallic substance, even if mystical in nature, that is detectable by mortal technology. 
The Eye's origins are currently unknown, but there are theories of how it came into existence. Some believe that it was discovered by Agamotto among the skies and stars, where it had drifted for ages. Others claim that it was created by Agamotto himself, which makes sense when the Eye's powers are compared to those of "the All-Seeing."
It is said that the Eye of Agamotto draws on Agamotto's own mystical ability to span distances and dispel disguises and illusions. Agamotto is also presumably aware of every time the Eye is used and may even record those events for later viewing.
Though Strange at first retained both the Eye and the Cloak, the Hood (at Dormammu's command) targeted Strange to eliminate him and seize the Eye of Agamotto. Strange, who had stepped down from the title of Sorcerer Supreme after his unwise use of Zom's power, refused to surrender the Eye, telling the Hood that he cannot use it because of his tainted soul and demonic connections.
After fleeing to the New Avengers, Strange described the Eye as "one of the most powerful mystic conduits on this physical plane". The team joined him in his search for new potential candidates. Dormammu sought the Eye for his own dark purposes, either to destroy it out of contempt for his ancient foe or to grant it to the Hood for more power. Over New Orleans, the Eye vanished from Strange's possession and presented itself to the new Sorcerer Supreme, Jericho Drumm (Brother Voodoo). As his first act of office, Voodoo defeated Dormammu, broke his connection with the Hood, and saved the New Avengers, Daimon Hellstrom, and Doctor Strange.
Agamotto inexplicably attacked the world, trying various ploys to bring the Eye to the Light Dimension, apparently unable to take it by force. Brother Voodoo challenged Agamotto for the eye, sending a mystically-empowered Wolverine as his champion. When Daniel Deyll, who was held captive in the Light Dimension, witnessed the battle turning against Wolverine, he intervened: Jericho took the Eye and engaged Agamotto personally, repelling the entity at the cost of his own life.
The Eye was later given back to Doctor Strange when he proved himself once again worthy of the mantle of Sorcerer Supreme.
The Eye is used to find and show 'truth.'
- It can emit an 'all-revealing light.'
- It can play back recent events.
- It has other abilities which are similar to telepathy but are magical rather than psionic, greatest of which is the ability to give its user certain mystical perceptions into another's soul.
- It accompanies the wearer's astral form and is one of the few items usable in either state (albeit at a less powerful state).
A 'third eye' often appears on the forehead of the wearer when it is used.
The Eye is used for order or "white" magic only. It does not respond to an evil user's commands, and can only be utilized by a magician of a pure heart and clean soul. However, there has been certain, unclear exceptions, such as when Baron Mordo, when disguised as Strange in a former masked costume he had donned, was capable of wearing both the Eye of Agamotto and the Cloak of Levitation. Strange also worked desperately during the brief conflict to cover the Eye’s gaze, seeming to believe that his impostor could somehow bend his will to the amulet. Mordo uses the Eye to detect the "ethereal vibrations" of the Ancient One in the chamber, even willing it to implant itself upon his forehead. The malevolent Asgardian deity Loki has also worn and used the Eye of Agamotto and the Cloak of Levitation when Thor established his rule over Earth. In the What If? Age of Apocalypse, Nate Summers uses the stolen Eye of Agamotto to create a portal through time to stop Legion, but apparently not even through the magic of the Eye does not autmatically bend the rule of diverging timelines, as is shown when, like a cancer, other realities in the Multiverse also become an Age of Apocalypse. The Silver Dagger also was able to steal the Eye of Agamotto after killing Strange.
The Eye can radiate a powerful mystical light that allows Strange to see through all disguises and illusions, even those of Skrulls (before the genetic engineering experiments that shielded them even from the magics of a Sorcerer Supreme), see past events, and track both ethereal and corporeal beings by their psychic or magical emissions. The light given off by the Eye also weakens a variety of evil mystical beings, such as demons, devils, undead beings, dark extradimensional entities, and even sufficiently corrupt human practitioners of the Dark Arts, as well as used by Strange in the past to achieve nothing more than nothing but mere yet wide and convenient illumination. Strange can use it to probe the minds of others, project a powerful mystical barrier, and create portals to other dimensions. It is also dimensionally linked to the Orb of Agamotto, Clea having used the latter to send Daimon Hellstrom and Power Man through it to Strange's Eye. It has also been used to place beings into suspended animation, and Strange has used its light to levitate objects as heavy as the Hulk and Professor Xavier plus his wheelchair together, or the Thing, with minimal effort while simultaneously magically controlling the Cloak of Levitation to fly himself, carrying a total of at least fifteen hundred pounds, during the early years of the Defenders.
The Eye of Agamotto can be used to transport a group of dozens of beings of all kinds and power levels into another point within a universe, as Strange did to combat the threat of Thanos. The Eye was used by the Ancient One to banish the demons worshipped by the Devil-Slayer's cult, and appears to be capable of being stolen by them without the Sorcerer Supreme's consent, to be used to unseal a dimensional doorway to the Earth dimension from the demonic dimension; Vera Gemini was able to use the power of the Eye of achieve Xenogenesis in one day whereas the demon overlords achieved it after many eons. The Eye was also used to pierce the veil of the Dark Dimension by opening a portal. The Eye of Agamotto automatically displays to Strange and the New Avengers through its arcane powers in the Quinjet at least thirty-five images of "those who would replace" Strange, suspended in floating and shimmering blue bubbles of light, before the Eye itself vanishes from Strange to the new Sorcerer Supreme. Strange also used the Eye to at least in one instance to project a bolt of pure mystic force (when Strange was confronted by both the Panther and Mantis over the Evil Eye fragment), even when T’Challa had prevented him from uttering invocations or performing gestures, proving that the Eye can be activated by will alone. Strange also joins portions of the combined life essences of himself, Valkyrie, the Hulk and Namor to weave a complex spell through the Eye, which channeled the life energies into a healing glow it bathed upon the dying Nighthawk, healing him. The Eye, on Strange’s command, has been shown to implant itself on the foreheads of other, non-mystical beings and affect them as well, conjuring a psychic illusion making the Hulk and Namor see the other as he is not. The Eye of Agamotto has also been utilized on at least one instance to "reverse the flow of time," causing a broken statue to be reassembled perfectly, though time was only twisted around the statue. Strange uses the Eye of Agamotto to show Nebulon an insight into mankind, mentally displaying to him man’s history, passions and achievements, ultimately dissuading him from further opposing Earth.
Curiously, Doctor Strange, even in his astral form, was able to swiftly conjure another Eye of Agamotto and Cloak of Levitation along with his own garb for Howard the Duck (without spoken incantation), which the duck was able to command, despite his lack of Sorcerer Supreme title. 
The Eye of Agamotto is interestingly shown to open itself partially or wholly even when not used, mostly during significant events or battles.
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