The fact that earth is not already crawling with aliens (no disrespect intended to the Aldebaranian's mode of locomotion, its just an expression), combined with the lack of an unambiguous signal received by any of the SETI telescopes, is sometimes referred to as the Great Silence, or the Fermi Paradox.
|I think this is from the brilliant comic XKCD, if you know otherwise please let me know!|
Another possibility is that interstellar space travel, either for reasons we do understand or for reasons we do not, may simply not be feasible. This is also uncomfortable for us, but it may be true. It is almost certainly true that crewed space travel will never exceed about 10% of the speed of light, for a variety of reasons (not the least of which being that by 12% of the speed of light, a grain of sand hitting the vessel would react with the force of a hydrogen bomb). But at 10% (or even 5%, which we have the technology to achieve right now) of the speed of light we could get to the nearest stars within a human lifetime. But there may be barriers to traveling through interstellar space which we haven't even considered.
Another possibility, one championed by UFO enthusiasts, is that our skies and streets ARE crawling with aliens, we just need to pull our heads out of our recta and realize it. This isn't quite as far-fetched as it sounds; some have posited that the natives in Hispaniola could not see Columbus's ships until their shamans or whatever they're called there did. This may be apocryphal, but it is true and demonstrable that the human mind filters out data it isn't prepared to process. If this sounds like BS to you, take this simple test here, and then come back to this post. My personal feeling is that this possibility is pretty unlikely, but I wanted to include it specifically because so many discussions of the Fermi Paradox willfully exclude it, which is simply bad science.
Yet another possibility is that alien civilizations have visited here in the past, and then (tinkered with chimpanzi genes to invent us/used their antigravity technology to move around a bunch of rocks/put on funny hats and modeled for neolithic artists/figured we were beyond hope and left never to return/fill in the blank). This is also possible; there is an entire field of research called SETA, or the Search for Extraterrestrial Artifacts. SETA to date has not proven any more fruitful than SETI, with one possible exception which I'll talk about in a moment. In order for an artifact to be unambiguously "alien" it needs to be something truly beyond the abilities of human artificers to construct. For example, the pyramids at Cheops are amazing, but well within the capability of bronze-age builders if you happen to have many of them. If the pyramids had been made out of titanium, for example, THAT would be a pretty good indication that it was not built by bronze-age humans.
One type of artifact especially interesting to SETA researchers is something called a Bracewell Probe, first proposed by Ronald Bracewell in 1960. It is an autonomous robot probe used essentially as a message in a bottle to another star, which has crammed into its memory banks all of the information from and about the originating species that it's creators deemed worthy to put in it. If the probe happens to have the ability to utilize resources in other star systems to self-replicate, it is called a von Neumann probe and then has the ability to cover a lot more interstellar territory. Arthur Clarke, in his novel and then movie 2001: A Space Odyssey, imagined that an advanced alien civilization might send out millions of such probes to monitor promising worlds around the galaxy. Rather than try to analyze the development of each of the billions of species the probes were monitoring, the aliens set up a simple test. They placed a Bracewell probe on the moon. Any species on earth which advanced to the point of landing on the moon would find the probe, and trigger it to give the previously earthbound species further instructions.
If you watched 2001 but didn't quite understand what was happening in that scene, or in any part of the movie, that's okay. Clarke was brilliant, and director Stanley Kubrick was brilliant, but the combination of the two of them was just effing weird.
So, we've been to the moon, and haven't found a Bracewell probe there. But oddly enough, we may actually have found one even closer than the moon.
On 6 November 1991 astronomer Jim Scotti discovered what he thought was a small near-earth object (asteroid), which was prosaically named 1991vg. NEO expert Duncan Steel at the University of Adelaide, Australia, analyzed 1991vg and made a truly startling discovery. Based on the orbit of 1991vg, which trails the earth in its own orbit but sometimes closes range with earth for brief periods and then resumes its "station" behind it, and based also on the fact that light reflected from it indicates that the object is of a faceted nature (more like a shoebox than a basketball), there are three possible explanations for it. The first is that it is a naturally occurring asteroid. The second is that it is a piece of human-made space debris, left over most likely from the early Apollo missions. The third is that it is a self-propelled artifact of non-human origin. Through careful analysis and process of elimination, the third possibility has emerged as by far the most likely candidate. Really.
It is important to understand that Duncan Steel is probably the world's foremost expert of NEOs. He has written dozens of papers on various aspects of NEO research, and Steel and Scotti together have discovered and catalogued more NEOs than maybe all of the other researchers in the field combined. When Duncan Steel says "that's definitely not an asteroid and probably not human-made space junk", it's worthy of further investigation.
Here is his paper on the subject, in its entirety: SETA and 1991vg
More research, obviously, must be done to determine the true nature of 1991vg. But if you happen to look up in the sky some night and see a giant baby swatting at satellites, don't say I didn't warn you.