The "illuminati" (meaning the enlightened in latin) is a name that was given to differents secret groups both fictitious and real. Historically speaking, the term illuminati refers to the bavarian illuminati, a secret society that operated for a whole decade. Its goals was to teach philanthropy and other secular values to the elites so they could make the rights calls when they had the power.
The illuminati did alot of unusual things, like using symbols (like an owl, an eye) and used pseudonyms to keep each other's identity hidden.
Historians assure that the illuminati failed to control the world unlike what the conspiracy theorists think. As stated earlier the illuminati operated for a decade then they vanished.
Illuminati as we know it today is just an internet joke (meme) to make fun of conspiracy theorists, like the usa congress is ruled by jewish lizards: It's just jokes.
TL;DR no they don't exist.
Oh okay Great article