The Illuminati currently appear in Jonathan Hickman's New Avengers and are dealing with colliding universes that could lead to the end of everything! They currently consist of Tony Stark, Reed Richards, Dr. Strange, Black Bolt, Beast, T'challa and Namor.
The Illuminati was formed after the Kree-Skrull War, by Iron Man, Namor, Mr. Fantastic, Professor X, Black Bolt, and Doctor Strange. After the Kree-Skrull War, Iron Man realized that if the six had worked together, they could have each used their own respective information and stopped it. Along with Black Panther, he proposed a government of superhumans. However, many of them refused, for individual reasons.
Namor-Many superheroes are violent, dark, or have criminal streaks.
Professor X-This will result in public resentment, fear, and hate against heroes like there already is against mutants.
Doctor Strange-Heroes are anti-establishment-they will never want to work with one.
However, the group(except Black Panther) formed the Illuminati and agreed to meet often to exchange important information.
Important Story Arcs
The Illuminati was responsible for launching Hulk far out into space, which gave him desire for vengeance and which led to the World War Hulk event.
When Iron Man introduced the Superhuman Registration Act to the group(which triggered Civil War, only Mr. Fantastic agreed with him. They all took their own positions on the event.
Namor-Originally had no position and didn't care, but eventually sided with Captain America. He sent an Atlantean war party to help him at the end.
Doctor Strange-Avoided the conflict. He spent the time fasting in the Arctic and praying that whichever side won would cause less pain and death.
Professor X-Was busy with House of M at the time, but when he returned, took a neutral stance with the rest of the X-Men.
Black Bolt-Vehemently disagreed and announced cold war between the US and the Inhumans.
The Civil War disbanded the Illuminati, each member going their own separate way.
After Civil War ends, it is revealed what the Illuminati were up to between their formation and the team's disbanding. Mr. Fantastic had managed to get the Infinity Gauntlet and a few of the Infinity Gems. He found the rest and proposed to keep it safe so villains like Thanos could never possess it again. When Reed finds he cannot use the Gauntlet to will itself out of existance, he disperses the Gems among the Illuminati for safekeeping. Mr. Fantastic holds onto the Power Gem, Professor X the Mind Gem, Doctor Strange the Soul Gem, Namor the Time Gem, Iron Man the Reality Gem, and Black Bolt the Space Gem, with each of them swearing never to use the gems.
After the Secret Wars, it was brought to the attention through the psychic abilities of Professor Xavier, that the cosmic force known as the Beyonder was actually the result of a mutant/inhuman receiving treatments from the Terrigan Mist. The Illuminati (minus Tony Stark, whose role as Iron Man was presently being filled by Jim Rhodes) decide to confront the Beyonder, but they are struck by his powers and are able to live their greatest fantasies. Despite the Beyonder offering such 'gifts' as allowing Black Bolt the ability to speak normally, they are able to overcome their desires and ask the Beyonder to leave. They convince the Beyonder to quit tampering with the earth when Namor speaks on Black Bolt's behalf as the King of the Inhumans. The Beyonder would disappear into a dust and the Illuminati would leave believing the day was saved...
Members and Representing
Each member of the Illuminati represents a different aspect of society and point of view, which is part of the reason they formed. Each member is also considered to be an unparalleled master of their domain or area of expertise.
Iron Man (Tony Stark): The master of technology and a founding member of the Avengers. Represents the technological and military/industrial communities. Also represents the Avengers and the type of hero who would work with the government.
Namor: The master of the oceans. Represents the underwater realms and Atlantis. Also represents the anti-hero.
Mr. Fantastic (Reed Richards): The world's greatest scientific intellect and the leader of the Fantastic Four. Represents the scientific and intellectual community.
Professor X (Charles Xavier): The world's most powerful mutant mind and the founder of the X-Men. Currently deceased, he represented the mutant population and community.
Black Bolt (Blackagar Boltagon): King of the Inhumans. Represented the Inhuman population and community. Also represented royalty. After Black Bolt's death, his widowed wife Medusa, Queen of the Inhumans, took his place in the Illuminati.
Doctor Strange (Stephen Strange): The master of magic. Represents the mystical/magical community and population, as well as that edge of society.
Captain America (Steve Rogers): The first true super soldier, an unparalleled leader, and master military strategist. Represents the American ideal. After the crisis involving the Hood obtaining a portion of the Infinity Gems, Captain America was invited to join the Illuminati. He agreed after realizing that some things were meant to be kept secret.
Beast (Hank McCoy): Current representative of the mutant population and community after the death of Charles Xavier in Avengers vs X-Men.
On Earth-23099; Captain Mar-Vell, Shuri and Magneto were also members of The Illuminati and were the last heroes to stand against The Black Priests, a group of immensely powerful cosmic beings who have been creating incursions across the Multiverse.