The Fermi paradox says that even if life is highly improbable overall, the size of the universe and the time in which it has been in existence should have led to many intelligent civilizations. In other words, if only a fraction of a single percent of grains of sand are red, but you're dealing with billions of grains of sand ... that's a lot of red dots.
So where are all the aliens?
This video does a good job of playing with some of the reasons we may not have seen any evidence of alien life, and it's certainly a fun thought exercise. You can also pretty easily come up with other scenarios; perhaps other civilizations know we're here and simply have us quarantined, allowing nothing in or out of a relatively minuscule pen of our galaxy. They may not be destroying other civilizations, just keeping them separated to avoid conflict.
This is also going on the assumption of an Earth-like planet spawning a sort of intelligence that kind of looks and acts like ours. For all we know there is super-intelligent life that's perfectly happy swimming in the ammonia of a gas giant, passively feeding and composing epic sonnets.
It's fun to think about, and I'd hate to think we live in a giant graveyard of past civilizations or, even worse, we're all there is.
