The Illuminati was an ancient secret group of scientists driven underground by the Catholic Church. The group was dedicated to pure science and considers the Church to be "spewing superstition." Its members include Copernicus, Galileo, and Gian Lorenzo Bernini.
The group accept inductees after going through the Path of Illumination; aspirants were required to follow a series of subtle clues left in various churches in and around Rome. The clues indicate the secret meeting place of the Illuminati.
During the events of Angels & Demons, the Illuminati were allegedly behind an attempt to destroy Vatican City during a papal conclave with a antimatter bomb. However, the Illuminati was long extinct and having been absorbed into the Freemasons. In reality, the true perpetrator was revealed to be Camerlengo Carlo Ventresca, who fabricated the Illuminati threat.
The real-life Illuminati was an Enlightenment-era secret society that was founded in 1776. Its members were politically minded freethinkers with no particular interest in science. Although the society's goals were to oppose religious influence, there were no “vows of revenge” against the Church for “crimes against scientists like Galileo and Copernicus.”