We've already discovered hundreds of exoplanets in other solar systems, but so far we haven't discovered a single extrasolar moon. It may just be because they're much harder to find - or because more extreme gravitational forces make them impossible.
The majority of exoplanets we've discovered are known as "Hot Jupiter" planets, because they're Jupiter-sized gas giants that orbit very close to their star, often much closer than even the distance between Mercury and our Sun. New computer simulations suggest that, as these gas giants got dragged towards their star in the early days of these alien solar systems, any moons the planets had would have been destroyed or ripped away from the planet.
Astronomers are still interested in searching for hidden bodies in these solar systems, even if the chance of the Hot Jupiters having moons is practically nil. A lot of astronomers are interested in the search for what we might call a "Warm Jupiter", a gas giant located roughly the same orbital distance as Earth. That would be far enough away for moons to exist, and in fact those moons would likely have a temperate enough climate to support life.