"is" may be the wrong word, since the Bavarian group collapsed in the 1780's. However, it is often speculated that it merely went underground, and some hold it responsible for many world events right up to the present day. However, here, I'll stick to documented events. The founder was Adam Weishaupt, who had joined the Freemasons in 1774, but became disillusioned and dropped-out. Instead, on May 1st, 1776, he created the Bavarian Illuminati, consisting of 5 members devoted to promoting equality & rationality, primarily through study. In 1777 Weishaupt re-entered the Freemasons, seeking lore for his own Order, and perhaps recruiting new members. Gradually, the idea was conceived for Illuminati to take control of Masonic Lodges and initiate Masons receptive to Illuminati ideas, and by 1783 the Illuminati had spread to Bohemia, Milan, and Hungary. In 1784, however, a high Initiate went public with sensationalist stories of his experiences, and the Bavarian Elector published an Edict forbidding secret societies. Despite Weishaupt's efforts, a subsequent Edict explicitly condemned both Freemasonry and Illuminism on religious, social and political grounds. Weishaupt fled into exile and the Illuminati vaporized. There, the trail grows cold, and we enter the realms of conspiracy theory. But, you never know... :-)

They were caught and no longer exist, there is a group that claims that they are descended from the Illuminati, they may follow their code, but they are not in anyway a part of the original group.