The Fermi Paradox basically goes like this: the universe is billions of years old, there are a huge number of planets (\(10^{24}\) according to this article) in the universe,  and probably a few of these planets have Earth-like conditions, so where are the aliens? Surely in a few billion years some of the planets would have developed intelligent life, and that intelligent life would have travelled the universe long enough to bump into us at some point.

But of course, it's entirely possible that intelligent life is so improbable that it's only come up in one of those \(10^{24}\) planets. This seems to be the most common 'solution' to the Fermi Paradox.