There's a story about Enrico Fermi chatting with Edward Teller, Herbert York, and Emil Konopinski, whilst walking for lunch. They discussed UFO reports, when suddenly Enrico Fermi, out of the blue, said "but where is everyone?"
The Fermi paradox goes something like this: Humans are sending out all sorts of signals into space, which can be picked up by far-away star systems. Thus, if there are aliens with highly advanced technology, they should be able to see that we're here on Earth. Vice versa, if alien civilizations, like us, are sending out radio signals into space, then we should be seeing them. So why haven't we found any aliens?
There are between 100 and 400 billion stars in the Milky Way, each with anywhere between 1-20 planets. A huge number of those planets contain water and are at a hospitable distance away from the star, just like us. So the Milky Way should be teeming with life. Even more puzzling is that some of those alien communities should be much more advanced than us and could've started populating the Milky Way. But if so, why does everything look dead?