The Living Tribunal is a vastly powerful humanoid cosmic entity who has existed as long as the universe itself. Its function is to safeguard the Multiverse (the total sum of all alternate universes) from an imbalance of mystical forces. It may act to prevent one universe from amassing more power than any of the others, or from upsetting the cosmic balance in some way. The Tribunal may also act to prevent an overwhelming imbalance of good or evil within a universe. When a matter involves only one universe, the Tribunal may leave the final judgment to the "abstract" entities there (in Earth-616's universe, Lord Chaos and Master Order). The Living Tribunal doesn't possess alternate counterparts, as there is only one Living Tribunal in the Multiverse.
If it means preserving the mystic balance, the Tribunal has the power to obliterate an inhabited planet. It can turn a star into a supernova with a single force bolt.
The Tribunal manifests itself as a being with three faces, which represent the three sides of the Tribunal's personality. Its front face, through which it usually speaks, represents equity, the fully hooded face on its right side represents necessity, and the partially hooded face on its left represents just revenge. All three voices must agree in a case before the Tribunal can intervene.
The Living Tribunal's first known encounter with a being of Earth-616 was with Earth's Sorcerer Supreme Doctor Strange. He later met Rom and the Beyonder. The Tribunal sealed off an alternate Earth devastated by Korvac, encountered the Phoenix of an alternate Earth devastated by S'ym and the Goblin Queen.
In a future timeline encountered the Hawk God and the Guardians of the Galaxy. The Living Tribunal and the Cosmic Congress were responsible for banishing the Hawk God from their midst, which inadvertently led to the origins of Starhawk and Aleta.
When Adam Warlock came into possession of the Infinity Gauntlet, the Tribunal told Warlock he couldn't wield that much power, leading to the creation of the Infinity Watch. Although the Tribunal refused to allow Warlock to wield the Gauntlet, he also ruled against Eternity, who wished the Gems to be placed under his direct supervision.
When The Stranger teleported the Earth of the New Universe to the mainstream Marvel Universe, the Tribunal sealed it off and imprisoned Quasar's girlfriend in there due to the threat the Star Brand had on the balance of power.
He also allied himself with his closest counterpart of the DC Universe, the Spectre, to save their respective universes from being destroyed by two cosmic "brothers".
Although his own duties are purely cosmic in scope, the Living Tribunal maintains a lesser conclave of judicial officers known as the Magistrati to rule on less dire matters.
Uatu and Iron Man found the Living Tribunal on the Moon, having been killed by the Beyonders, and landing on every reality, one sliver of itself for each universe.
The Living Tribunal may or may not have been defeated when Thanos claimed the power of Heart of the Universe for himself, and seemingly absorbed the Living Tribunal, along with Eternity, and Infinity. However, given that Thanos only absorbed and recreated a single universe, whereas the rest of the multiverse suffered no effects from his actions, it was likely just a Manifestation Body/weak avatar of the Tribunal.
This interpretation was validated by Marvel's executive editor Tom Brevoort, who stated that like all, "The End" series, the story was intended to have no effect whatsoever on continuity, and if it had, Death would have been made absolute again, which it was not. So the entire event may also have taken place as an "imaginary story" completely outside of Marvel's multiversal continuity.
The Living Tribunal once asserted that it had a fourth face, but that aspect of its being split off to become an independent entity known as the Stranger. The Stranger denied this, and truth remains open to interpretation.