Adamantium is an Virtually-indestructible metal used by many people for experiments.
Stryker and the Weapon X team then proceeded to inject the adamantium into the skeleton and bone claws of Wolverine, making him nigh-indestructible. When he is later shot in the head with bullets made of the compound, he sustained severe intra-cranial trauma that induced extensive amnesia.
Later on, Wolverine's memories began to return to him, and by the time of the events that occured in The Wolverine, he managed to regain much of his lost memories. And by the time of the events of X-Men: Days of Future Past, he appears to have regained all of his lost memories.
The adamantium in Logan's body was actually poisoning him, this was kept in check by his healing factor. However, by 2029 Logan's healing powers were weakened and thus the metal began to poison Logan's body, leaving him in a state of constant pain. Logan also kept an adamantium bullet with him out of temptation of suicide. The bullet was later used by X-23 to kill X-24 instead.
Stryker later gave similar claws to Lady Deathstrike, his controlled bodyguard, extruding from the tips of her fingers. However, in a battle with Wolverine, he defeated her when he impaled her with an adamantium needle which pumped her body full of the indestructible alloy and she fell to the bottom of the Weapon X tank.
When Ichirō Yashida became ill and on the verge of death, he began stockpiling adamantium reserves at his facility in the north of Japan to construct the Silver Samurai armour as a life support system in the interim period before Wolverine was captured. He ordained the capture of Wolverine so that he could cut through Logan's adamantium claws using a heated adamantium blade and distill Logan's healing powers into his own body in order to live forever.
The katana swords that the Yashida Clan had within their possession in their household were also likely made out of adamantium, as it has been proven that regular steel cannot cut adamantium.
At some point during the Transigen Project, X-23 was grafted with adamantium claws.
- Although William Stryker stated in X2: X-Men United that adamantium became indestructible once it cooled, it has been proven that, if adamantium weapons are super-heated they are capable of damaging other adamantium weapons, i.e., cutting off Wolverine's adamantium claws.
- In Logan the adamantium poisoning that Wolverine is suffering from symbolizes his own personal conflict within himself. Hugh Jackman revealed "The adamantium will eventually kill him. I loved the metaphor of his weapon being the thing that's killing him, on every level." 
- ↑ 1.0 1.1 1.2 X-Men Origins: Wolverine
- ↑ 2.0 2.1 2.2 The Wolverine
- ↑ X-Men: Days of Future Past
- ↑ Logan
- ↑ 5.0 5.1 X2: X-Men United
- ↑ Empire Magazine: March Issue 2017 - Page 64 Hugh Jackman Reveals Empire's Exclusive Logan Cover