There is a contradiction between the high probability estimates for the existence of life outside Earth and the absence of evidence for it. This contradiction is known in astronomy as the “Fermi paradox” and follows the line of reasoning below:
There are about 100 billion stars in the Milky Way galaxy, many of which are similar in size and stage of evolution to our sun.
Hundreds of millions of these stars likely host Earth-like planets, and if life evolves similarly on these planets, some may have evolved intelligent life.
With civilizations that are perhaps millions of years more advanced than us, it is likely that they have developed some form of interstellar travel.
The famous 'Drake Equation' is closely tied to the Fermi paradox. It calculates the approximate number of extraterrestrial (ET) civilizations in our galaxy and can pump out some huge numbers (due to the vast number of potentially habitable planets in the galaxy). When used by optimists, the Drake equation produces numbers between 1,000 and 100,000,000 civilizations within our galaxy alone.
So where are the visitors? We have seen no sign of extraterrestrial life, we have not heard from them, and they have not visited. One of my intellectual heroes Nick Bostrom (Oxford) claims that our lack of evidence for ET intelligence supports the idea of a "Great Filter", which essentially serves as a probability barrier for evolving species. He claims that since, statistically, we should have been contacted by ET life but haven't been suggests that it is very, very improbable that evolution begins, or that the Great Filter lies ahead of us in the future (possibly in the form of superintelligent AI, nuclear destruction, etc...). The filter could be an obstacle that has stopped countless other intelligent species in their evolutionary tracks across the universe, so we must hope that we have already passed it or are able to circumnavigate it when we arrive.
Of course, there are other hypothetical explanations for the lack of alien visitation. These range from ET life deliberately avoiding us (haha) to extraterrestrial intelligence being entirely different from ours (i.e. they are “too alien”). Some theorists even entertain the idea that they are here already, unacknowledged, living amongst us…