High Lords of Terra

The High Lords of Terra are the rulers of the Imperium, who act in the Emperor's stead while he is unable to speak.

Official Canon
Each of the high lords represents a specific branch of the Imperial government, and while they are generally capable of running their own branches without much interference, they still need to convene on matters of policy that affect the Imperium as a whole. However, by the 41st millenium, they have grown into incompetent bureaucrats who tend to make things worse for the citizenry.

The incompetency of the High Lords had been known as early as the War of the Beast in M32, when the various High Lords refused to do anything constructive, and some openly attempting to placate the Orks to maintain their power. Eventually they were all killed by the leader of the Officio Assassinorum in an event known as the Beheading.

TTS Canon
While there are more members of the High Lords, the four that meet the most regularly are the Grand Provost Marshal, the Commander Militant, the Master of the Administratum, and the Fabricator-General. The four were picked up from the Old Folks' Planet to run the Senatorum Imperialis, though they spend most of their time making things illegal, such as breathing, and keeping laxatives for themselves. They're not actively malicious, they're simply extremely senile and unaware that laws could be used to benefit other citizens of the Imperium.

The High Lords were eventually made obsolete when the Emperor started speaking again, and eventually made it illegal for them to make new laws to put a stop to their antics. Magnus attempted to have them assassinated so that he could rule the Imperium in their stead, but the men that Kitten shot turned out to be Lacrymoles instead. The Fabricator-General soon after left for Mars to throw a party.

The Grand Provost Marshal, head of the Adeptus Arbites, is obsessed with the law, constantly shouting "I AM THE LAW(N)!" He was the one most devastated by the Emperor's decree banning new laws. The Grand Provost Marshall even obsesses over game rules, having read the full games tomes for Warhammer Fantasy Roleplay and interjecting whenever Magnus or one of the players broke the rules. His character was an Imperial Magistrate named Brukham Nougat, who likewise was obsessed with the law, but found himself broken by his experiences in the Mountains of Mourn.

The Commander Militant, head of the Imperial Guard, seems to be the least senile of the bunch, as he's able to keep the interests of his generals and soldiers (and by extension, the Imperium at large) safe from the whims of his ban-happy peers. He is also a pimpin' gangsta in his spare time. During the roleplay game, the Commander Militant played a character named Kräkus who was obsessed with collecting and throwing dung. He was killed by The Gorger Lord, in a way that denied the usage of his fate point.

The Master of the Administratum is fixated on keeping his bowel movements regular, but otherwise isn't terribly inept. Unlike his peers, he eagerly looked forward to a well-earned retirement. His roleplay character was a Halfling named Bulgo Potatoskin, who was one of the more reasonable party members, and was extraordinarily lucky with his slingshot, but was eventually also killed by the Gorger Lord.

The Fabricator-General, head of the Adeptus Mechanicus, always speaks in auto-tuned melodies and complains that his fellow High Lords don't have enough cybernetic modifications. He is unable to say "buttcheeks," as it causes him to self-destruct. He was completely fine in the next scene, which was later explained that he was secretly in possession of the Proteus Protocol and was using it to stay alive forever. And like his fellow Tech-Priests, he's obsessed with toasters. While he initially appears to be similar in stature to his fellow High Lords, his lower half is actually a massive room-sized machine. It is implied that people in the High Lords' chamber are actually standing on top of him. He was last seen being brutally slammed by Asmodai in repentance under Azrael's command over a copy of a Dark Angels book that was earlier thrown to him by Cypher.

Other High Lords
Other members of the Imperium who count as High Lords are:
 * Ecclesiarch Decius XXIII, head of the Adeptus Ministorum
 * Little Kitten, Captain-General of the Adeptus Custodes
 * Fyodor Karamazov, the Inquisitorial Representative