Many of the most interesting bodies in our Solar System aren't planets, but the moons that orbit them. And, as far as we can tell, the physics of the processes that produce large planets should make moon formation inevitable. Yet, despite some tantalizing hints, we've not found a clear indication of a moon orbiting an exoplanet. What we have found are a few very young exoplanets that appear to have moon-forming disks around them. That's despite the fact that the star it's orbiting seems to have a planet-forming disk that's mostly water.