The Illuminati is a mysterious secret society that manipulates the world behind the scenes.
Percival founded what would eventually be known as the Illuminati Society in or around the year 642, roughly a century after the "death" of King Arthur Pendragon, in order to "make things right".  He is still alive in modern times. ("Rock of Ages")
By the late 10th century, it had already developed its current name and its logo, a pyramid with a fiery eye at its summit (this same symbol also appears on the Great Seal of the United States, suggesting some sort of connection between the Illuminati and the Founding Fathers).  In 975, a temporally displaced Xanatos used this logo to identify himself as a member to the Norman Ambassador. Xanatos instructed the Illuminati to deliver a coin to a young David Xanatos in 1975 and a set of instructions to an older David Xanatos in 1995. Despite the thousand year interim, the Illuminati were able to follow these orders exactly as instructed. ("Vows") The Illuminati's overall history is as yet veiled in shadow (not surprisingly), but it is known that in 1924, they made Mace Malone go into hiding after he became their adviser on organized crime, to protect him from the syndicates.
In the 1990s, the Illuminati became aware of the gargoyles' existence through Xanatos, and began to hunt them, hoping to control them. Their first recorded attempt came when Mace Malone persuaded Matt Bluestone to lure Goliath to the Hotel Cabal; Matt helped Goliath escape and Malone became trapped in the hotel himself, but the Illuminati were apparently satisfied, enough so that they inducted Matt into the Society anyway. ("Revelations")
After the gargoyles were revealed to the public, the Illuminati entered into a partnership of sorts with Jon Canmore, helping him to set up the Quarrymen (which was already in the works) under the alias of "John Castaway" and providing him with the necessary funding, for their own as-yet-unknown purposes.  The fact that Thailog is a member of the Illuminati indicates that the Society has no intention of wiping out the gargoyles - though they let Castaway believe this to be their goal. The Illuminati also claimed to support Matt Bluestone's use of the Gargoyle Taskforce to protect the gargoyles, and Xanatos's plan to introduce the gargoyles to "polite society". ("Invitation Only", "Bash")
The Manhattan Clan are not the only people in the Gargoyles Universe who are due for clashes with the Illuminati. King Arthur and Griff will have a number of encounters with them during their quest for Merlin, and the Director set up the Redemption Squad in part as a means of battling the Society. One of the Squad's first missions was to strike the Eastcheap, though all that they succeeded in doing was capturing Mistress Quickly, one of Falstaff's henchmen; Falstaff and the Eastcheap got away. The Illuminati will also quickly become involved when the New Olympians reveal themselves to the outside world.  Although the gargoyles, King Arthur, and the Redemption Squad will all cause the Society a number of setbacks, it will not be destroyed or broken up - at least, not in the present. 
In 2198, when the Space-Spawn invade and conquer Earth, the Illuminati decide to throw their lot in with the invaders. They form a secret pact with the alien occupiers, agreeing to undermine any attempts by the conquered Earthlings to overthrow the Space-Spawn in return for the release of those of the abducted world leaders who were secretly Illuminati. It is unknown as yet as to whether Peredur is still the leader of the Illuminati at this point, when they advance from mere manipulators to quislings. 
Known members of the Illuminati, past and present, include Peredur fab Ragnal, Duval, Blanchefleur, the Norman Ambassador who accompanied Princess Elena to Castle Wyvern in 975, Quincy Hemings, Shari, David Xanatos, Mace Malone, Martin Hacker, Castaway, Thailog, Fiona Canmore, Falstaff, and Matt Bluestone.
There are thirty-six ranks within the Illuminati. At the very top is Peredur, the mysterious number one. The second rank is composed of Mr. Duval and Quincy Hemings. Each succeeding rank contains a number of members equal to the number of the rank (so that there are thirty-six members in the thirty-sixth rank, for example); this means that the total number of Illuminati would be six-hundred-sixty-six. (the Number of the Beast in the Book of Revelation). Not all slots are always filled.  New members always start at the bottom before working their way up.  Members across the centuries have identified themselves as fellow Illuminati with rings, tattoos, and/or lapel pins featuring the Society's symbol (tattoos, in particular, fell out of favor largely because of the risks they pose when it comes to deniability).  When Illuminati members hold secret meetings, they open proceedings by stating their rank numbers. ("Masque")
Much of the Illuminati's ability to exert control seems to come from having members in strategic places (such as Quincy Hemings on the White House staff). In light of the hold that they acquired over organized crime through Mace Malone, blackmail seems to be another method. They also operate the Hotel Cabal in New York City as a device for breaking down the resistance of their prisoners and thereby wresting valuable information from them.
The Illuminati has also actively discouraged various conspiracy theorists over the years.  Matt Bluestone's own efforts to expose the Society while an agent at the FBI was (at least, initially) thwarted when Illuminatus Martin Hacker became his partner to guarantee Bluestone only investigated wild goose chases.
The Illuminati supply their older members, such as Mace Malone, with rejuvenation drugs that help prolong their life-span and recover or preserve a youthful strength and vitality. Evidently, the organization's dental plan is impressive as well. ("Revelations")
The Illuminati also operate a ship known as the Eastcheap, an island-size (and disguised as such) vessel which contains a vast amount of the Illuminati's priceless antiques and artifacts from around the world, run by their treasurer, Falstaff. ("Losers")
The goals of the Illuminati are, at present, unknown, though apparently these have something to do with King Arthur Pendragon's projected return at the end of the 22nd century (Peredur's discovery that Arthur had awakened two hundred years ahead of schedule shocked him enough to alert the upper echelon members), which coincides with the Space-Spawn invasion (see above). While they do reportedly control almost everything (Matt has claimed that even the President of the United States is their puppet - we do not know if this is true, though the recent revelations concerning Quincy Hemings have raised some interesting possibilities here), we do not as yet know what their purpose is in so doing.
Known Members and Numbers
- Peredur fab Ragnal - One
- Duval - Two
- Quincy Hemings - Two
- Fleur - Three
- Shari - Nine
- Martin Hacker - Thirty-Two
- David Xanatos - Thirty-Six
- Matt Bluestone - Thirty-Six
- John Castaway - Thirty-Six
- Thailog - Thirty-Six
- Falstaff - Unknown
- Fiona Canmore - Unknown
- Norman Ambassador - Unknown, possibly deceased
In the Radio Play, Tombstone was revealed to be an Illuminatus at the rank of thirty-six and Chameleon with the rank of thirty-five. Both of them conspired in a scheme with Thailog to acquire the Spear of Destiny and the Crown of Thorns, which were sent to Duval.
In the Radio Play, Vandal Savage was revealed to be an Illuminatus at the rank of three, and that he was the one who inducted Thailog into the Society.
The Illuminati were revealed to be an organization of arms dealers manipulating wars and conflict in order to profit off of them. They disguised themselves as a new clan of gargoyles that was also hiding in Manhattan to lure Goliath into a trap where he was captured and brainwashed by Dr. Nexus to assassinate Egon Pax. The plan was foiled. ("To Serve Mankind")
Real World Background
The Illuminati Society is a concept that has been around even before the creation of Gargoyles. While no doubt the belief in a secret society controlling events behind the scenes has existed for centuries, the particular name "Illuminati" dates from May 1, 1776, when one Adam Weishaupt founded a society by that name at Ingolstadt in Bavaria. The Bavarian Illuminati were Deists who saw themselves as truth-seekers; the Bavarian government, however, came to view them as a threat, and finally shut them down in 1785.
Rumor has it, however, that the Illuminati survived this attack, although going into hiding, and later on caused the French Revolution. In recent years, the notion of the Illuminati as still around and manipulating world events has become a popular one among conspiracy theorists, and even formed the basis of a Steve Jackson trading card game. Along the way, this popular image of the Illuminati used in Gargoyles came to absorb into its mythos both the Freemasons (drawing on the popular beliefs that the Freemasons are a sinister secret society that helped influence the Founding Fathers) and the Knights Templar.
The Illuminati's pyramid and fiery eye symbol is a common element of its mythos outside of Gargoyles, originating in the beliefs of many people that this design upon the Great Seal of the United States and the back of the one-dollar bill is the mark of a secret conspiracy connected to the foundation of the U.S. Peredur's role as the leader of the Illuminati may well be thanks to the connection of the Grail to theories about such societies.
The purpose of the Illuminati in conspiracy theories varies, although one popular one is that they plan to impose a Satanical dictatorship upon the world, in which Christianity will be abolished. (This is unlikely in the case of the Gargoyles Universe - though there is the "666 members" to consider.)
- Illuminati at Wikipedia, the Free Encyclopedia