Though rumors persist, it is unclear whether the the Order of the Illuminati established in May 1776 in Germany still exists. If it does, it is so secretive that membership details are not made public.
The term illuminati means "enlightened ones." The group that formed in 1776 comprised only five liberals and intellectuals who were tired of Roman Catholic rule in Bavaria. Their mission was to replace church rule with a republic. The organization was led by a law professor and wasn't so secret, though it was modeled after the very secretive Freemasons.
Within 10 years, the Illuminati had spread throughout Europe and had more than 10,000 members. The Illuminati was purportedly disbanded in 1785, or at least that is the last known date the group is known to have existed. It was disbanded after the German government passed a law forbidding the existence of any society that did not have its permission; the leader of the Illuminati was exiled at that time.
If the Illuminati has persisted throughout the years, then it has not asserted itself in the way the original group did. It is possible a new Illuminati has formed that is in no way related to the original. Again, however, there is no hard evidence to support such a theory.