A small exclusive group that lives sometime a few hundred years ago and I wouldn't be surprised if there were a few shadow or copy groups existing today. As for the extent of their power, I'd say their influence beyond social culture is minimal or null, most of their influence comes from the perceived idea that they are powerful, I hardly think they are though. Basically, I think the official grouped died out a long time ago, but I wouldn't be surprised if people have made groups calling themselves illuminati today, due to the stigma behind being part of such a group.
What's your explanation for "Dark Energy" and "Dark Matter"? Doesn't have to be scientific, I'm just asking what you think they are