Adamantium is an unbreakable metallic alloy, widely considered to be indestructible. The molecular makeup of adamantium defies scientific analysis, making the metal impossible to reverse-engineer. While various research facilities have samples of the ultra-dense metal, the process by which it can be molded is a virtually-unknown secret.
The Weapon X project successfully managed to bond adamantium to Logan's skeleton and claws, making the mutant soldier inhumanly durable and resistant to injury. The process was repeated with Deathstrike, the bodyguard of William Stryker.
With the death of William Stryker, it is unknown if anyone retains the ability to effectively weaponize adamantium. In 2006, Daniel Lyman kidnapped Scott Summers in an attempt to glean the possible secrets of the process from his subconscious, but was unsuccessful.
Outside of military uses, adamantium has been used for medical applications, namely scalpels and needles that can be used to pierce the skin of otherwise-invulnerable mutants. Rumors persist concerning "adamantium bullets", but the sheer cost and weight of such a projectile would make its use horribly restrictive.