The characters joined forces and secretly work behind the scenes. The Illuminati was established to exist (via story retcon) in their first published appearance in New Avengers #7 (July 2005), written by Brian Michael Bendis. Their history was discussed in the special New Avengers: Illuminati (May 2006). The group was revealed to have been formed very shortly after the Kree-Skrull War.
EHT Comics 