Hierarchs

The three High Prophets serve as the highest leaders of the Covenant High Council, being theocratic and known as "Hierarchs". The Hierarchs are thin, hunched creatures with large craniums that float on levitating Gravity Thrones decorated with golden backs, equipped with energy shielding and armed with Gravity Cannons. They wear crowns adorned with small holographic projections of Halo; they have the ability to access teleportation grids.

Prophet of Truth
Little is known about Truth, except that he is the remaining Hierarch at the end of Halo 2 who offered the former Supreme Commander of the Fleet of Particular Justice the chance to become the Arbiter and ordered him to defeat the Heretics, rebels that regarded Covenant teachings as false, and to retrieve the Sacred Icon on Delta Halo.

He spearheaded the purge of the Sangheili Councilors, which sparked the Great Schism.

When Gravemind teleported the Master Chief to High Charity, Truth betrayed Mercy, who was under attack by a Flood Infection Form. He prevented Tartarus from aiding Mercy and escaped to his Forerunner flagship, but not before Master Chief realizes his aim and pursues.

Aboard the Forerunner Dreadnought, Truth then led the Covenant Armada to Earth in order to activate the portal to the Ark. Once there, he set the Forerunner Ship at the base of Mount Kilimanjaro, and began excavating the Ark with Loyalist plasma bursts. Once activated, the excavation triggered a large, stable Slipspace portal to Installation 00. Truth took up residence in the Installation's Control Room in preparation for the Array activation.

Soon after, the Humans and Elites followed through the portal to the Ark. They took down the fortified defenses surrounding the Control Room and deactivated the shield protecting the Citadel just as High Charity exited the portal, spewing Flood forces in every direction. Flood projectiles crippled the Separatist flagship, the Shadow of Intent and prevented the Elite forces from being able to enact the planned mass assault against Truth's final forces. As a result, the Master Chief and Arbiter proceeded into the Control Room, unexpectedly aided by the Flood. The Arbiter then impaled Truth with his Energy Sword, finally putting an end to the deceitful Prophet and the triumvirate of Hierarchs.

Prophet of Mercy
The Prophet of Mercy is much older than any other known Hierarchs. Mercy was first seen during the trial of the Supreme Commander of the Fleet of Particular Justice, Thel 'Vadamee, and agrees with Truth to promote the disgraced Elite to the rank of Arbiter in a bid for redemption and the eradication of the Heretics.

Mercy, along with Truth, crafted the plans to invade Earth for the second time after the Prophet of Regret's initial botched invasion, this time perhaps to secure the Ark, begin the Great Journey, and wipe out the Human Race entirely. Before he can act, however, he is attacked by a Flood Infection Form on High Charity. Seeing this, Truth tells Tartarus to "let him be" and then tells Mercy, "The Great Journey waits for no one, brother, not even you." The Master Chief finds Mercy being consumed by a Flood Infection Form. Mercy then tells the Chief of Truth's plans. Master Chief, in return, kills the Infection Form, thus preventing the Prophet from suffering through the assimilation and preventing him from becoming infected. Mercy then collapses dead from the trauma of being attacked.

The Prophet is not seen after this, and is presumed to be destroyed when High Charity's reactors went critical, or when Installation 04 (II) exploded.

Prophet of Regret
The Prophet of Regret is the youngest of the High Prophets, and like all Prophets, his name is contrary to his true nature; he is reckless and headstrong, which leads him to commit actions that he should regret, but he doesn't.

Regret led the initial, failed attack on Earth with two Assault Carriers and a small contingent of battle cruisers. After one of the Assault Carriers was destroyed by the Master Chief, he ran through the gauntlet of MAC stations and landed troops in New Mombasa, part of the East African Protectorate, the only place the Covenant landed on Earth. After being repelled by marine forces, he initiates a slipspace jump to Delta Halo, destroying New Mombasa in the process. It is speculated that he was not at all aware of the centrality of Earth to Humanity and simply assumed it was another world that had, at one point, been inhabited or manipulated by the Forerunner. This accounts for his Fleet being far smaller and much less prepared than the Fleet that destroyed Reach and other high-profile colonies.

His actions did not win him a reprieve as Master Chief pursued him through Covenant forces on Delta Halo. Truth, in an apparent attempt to increase his power, called off reinforcement Phantoms, which gave the Master Chief a sufficient window to assassinate him.

However the Prophet of Regret makes a final appearance later in the game, revived to a degree by the apparent Flood leader Gravemind as a Prophet Form and argues with 2401 Penitent Tangent, condemning the ineptitude of the Holy Oracles. It is unknown how the Gravemind managed to retrieve his corpse, as the entire area was seared and destroyed by Covenant Energy Projectors immediately after his death.

Past High Prophets
The High Prophets are usually replaced all at the same time through political machinations. Previous High Prophets include the High Prophet of Restraint, the High Prophet of Tolerance and the High Prophetess of Obligation. These three hierarchs were disposed of when Truth, Mercy and Regret came to power.

Trivia

 * The song 'What I've Done' by Linkin Park has a line which mentions the names of the Hierarchs (Regret, Truth, Mercy). The lyrics go as so; "Cause I've drawn Regret from the Truth... So let Mercy come...". Though this is most likely a coincidence, the members of Linkin Park have stated they are fans of the game. Also, the song's album, Minutes to Midnight, is exactly 117 MB large.
 * A recurring theme is that the High Prophets personalities are opposites of their titles (i.e. Truth lies to the Covenant about the Great Journey, the Prophet of Regret never showed regret for his actions, and Mercy showed no mercy to the Arbiter).
 * Each of the three prophets were killed by a different enemy of the Covenant faction. Regret was killed by UNSC, Mercy was killed by the Flood, and Truth was killed by the Covenant Separatists.
 * The High Prophetess of Obligation is currently the only known female hierarch.
 * Despite prophets being rare you can see in each high prophet in gameplay with 2 being dead and one even facing as a boss.
 * All of the prophets in the era of the trilogy were eventually absorbed by Flood.
 * Prophet of Mercy was formerly the Philologist on the Forerunner Dreadnought, Prophet of Regret served as the Vice Minister of Tranquility, and the Prophet of Truth served as the Minister of Fortitude.
 * Despite their loyalty to the Prophets, some Covenant members do not totally agree about refusing to let Humans join them, some want Humans in the Covenant because they (Humans) are well known and respected for their bravery when seriously outnumbered, unlike Grunts for example, whether the Prophets would use Humans as cannon fodder (due to the war) or respect their intelligence and bravery may not be known.