Some say they exist as mere wraiths-- shadows representative of even darker forces. Some say they are definitely men. Powerful men, whose 'jobs' are to plot out the fate of the planet- using humanity as their game pieces.
Nobody (alive) can really explain their power structure, how they got started, who is in charge of them (as a group)- or even why they remain 'secret', and what they truly are 'master' of....
One speculation is they belong to, and founded, the (also) super secret group known as the Illuminati. Details of which are better read about in Robert Anton Wilson & Robert Shea's popular Illuminati Trilogy.