Is life that exists beyond the terrestrial biosphere. No conclusive evidence of extraterrestrial or "alien" life has so far been produced, in spite of numerous highly dubious claims to the opposite.
Most scientists seem to believe - and the research being conducted seems based on this prejudice - that life can only evolve on small rocky worlds containing carbon and liquid water - in short: planets all but identical to earth. While this argument seems reasonable based on the fact that Earth is the only planet so far discovered, that has a biosphere, it is the logical equivalent of sampling a cubic centimetre of water, finding no fish in it, and concluding that fish don't exist. The "SETI" or "Search for Extraterrestrial Intelligence" project listens to radio transmissions from other civilizations, and have so far been out of luck.
However, the success of this project is based on the assumption that life elsewhere will be somewhat like ours, develop radio-communication, and happen to beam a signal towards Earth.
This opens up for the Fermi Paradox , which is: "The apparent contradiction between high estimates for the probability of extraterrestrial civilization, and humanity's lack of contact with, or evidence for, such civilizations" The basic points of the argument are:
The sun is a young star. There are billions of stars in the galaxy that are billions of years older. If the Earth is typical, some of these stars likely have planets with intelligent life;
presumably some of these civilizations will develop interstellar travel, as Earth seems likely to do.
At any practical pace of interstellar travel, the galaxy can be completely colonized in just a few tens of millions of years.
The Observable universe is currently believed to have at least 80 billion galaxies.
According to this reasoning, the Earth should have already been colonized, or at least visited. Hence Fermi's question: "Where is everybody?"
However, advanced lifeforms might not use radio-communication, they might use technology beyond our current understanding of physics, there might be galactic laws against contacting species without the capability of interstellar travel, or they might not be interrested in us at all.
Stephen Hawkings is convinced that aliens exist and argue that we should keep our neck down, as he believes that a meeting between humanity at its current stage and a civilization with interstellar travel-capability, will be similar to the meeting between columbus and the indians, with Humanity being the indians.