According to the illuminatus! trilogy the illuminati are one of several secret societies that are competing for control of the world and, eventually, their ascension to godhood. Supposedly founded in Atlantis as an order-worshipping religion that caused the eventual destruction of Atlantis, far before the Bavarian Illuminati. They have turned up as the ruling class in Babylon, in the Muslim world as the Ishmealian sect or Hashashim, in Germany as the Bavarian illuminati, and later as part of the Nazi party and in France as a group of Masons that started the French revolution. They have orchestrated both world wars and many assasinations. However, much of this history is speculation, and it is never entirely revealed how old the modern-day illuminati are or what the correct history is, although in the books Atlantis definitely exists
They continue to exist today, controlling most of the world's media and business, and manupulating the general population to ensure docility so they can achieve their aims. They have almost complete control of world government, and many polititical activist groups such as Neo-Nazis. They aim to condition humans through teaching from an early age and use of drugs to unconditionally obey authority and therefore to make them easier to govern. The most dramatic example of this is the reaction to fnords, which they have inserted in almost every newspaper to create an atmosphere of fear.
They operate in a pyramidal power structure, which is ultimately controlled by five leaders called The Five. Initially recruits do not know the ultimate objective of the illuminati, and are told that they are aiming for some other objective, such as communism. More is revealed to them as they rise up the ranks. Much of the structure of the organisation is based on the number five, as it apparently exceeds the human ability to connect things, and makes the actions of the illuminati seem random and unconnected.
Their most famous symbol is the eye in the pyramid, as found on dollar bills, but they also often use shapes such as pentagrams or pentagons because of the law of fives.
They are opposed by a group of anarchist groups such as the Justified Ancients of Mummu, and the Legion of Dynamic Discord, who have allied to oppose the Illuminati and have also created front groups though which they combat the Illuminati. They use unorthodox methods such as drug use and Satanism, but are ultimately the more moral of the two groups.
This is all from the Illuminatus! trilogy, so any resemblance to real life is purely coincidental.