Adamantium is an indestructable metal used in 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 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.
Sabretooth wanted to be in the experiment that his brother was in. Stryker said he couldn't survive and rejected the deal after Sabretooth did what was asked.
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 got sick, he began stockpilling a lot of adamantium at his Laboratory to construct the Silver Samurai armour in order to keep him alive. He even had an adamantium sword which he had used to sever Wolverine's claws.
The swords that the Yashida Clan had within their possession were also likely made out of adamantium, as it has been proven that adamantium can not cut adamantium.
- Although William Stryker stated in X2: X-Men United that adamantium was 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.