Extrasolar entities are, by definition, biological (or possibly artificial) beings originating from outside of our own solar system. To date, no such extrasolar entities have ever been identified or made known to us in a verifiable and scientifically accepted way.
However, there is both a growing mountain of anecdotal testimony and a cottage industry in "UFOlogy" which maintains that highly advanced extrasolar entities have visited Earth for quite some time.
None of this evidence has been scientifically verified (the best case for the "UFO" aliens, in most cases, is that some cases cannot be given a natural and convincing alternative explanation). Nevertheless, speculative scientific investigation of extrasolar life is a small but growing field.
Note that this is quite different from extraterrestrial life: NASA and the European Space Agency have already devoted considerable resources to investigating the possibility that primitive life forms once lived on our nearest planetary neighbour, Mars.
Because we lack the telescope technology even to peer at the surface of extrasolar planets, let alone begin to guess whether those planets are populated, we really have no idea what extrasolar entities, if they exist, might look like.
Nevertheless, scientists are generally optimistic that, given the enormous number of stars in the galaxy (one hundred billion) and the likelihood that potentially life-supporting planets orbit even a small fraction of those, it is a statistical probability that there is other life out there somewhere.
The most interest in extrasolar entities, however, involves not just primitive microorganisms but life like us: intelligent, self-aware, technological, and socially organized beings. These beings, many belief, we can search for without necessarily spotting them directly.
That belief lies at the centre of the Search for Extraterrestrial Intelligence (SETI), for example, the primary project of which is listening to deep-space radio transmissions in the hopes of detecting signals of such regularity and complexity that they could never be emitted by a natural source such as a star.
In terms of scientific theory, two basic theorems underlie our current philosophy about extrasolar entities, both dating from the initial wave of excitement about extrasolar life in the 1950s and 1960s.
The first, the Drake Equation, is a rough attempt at estimating the number of intelligent extrasolar civilizations (i.e. alien civilizations) in our galaxy, based on the number of stars, an estimate of the number of planets, and the likelihood of the various conditions necessary for life being present on a given planet.
The odds against intelligent life arising, it is believed, are astronomical - however, in a galaxy which contains hundreds of billions of stars and presumably several times that many planets, many are prepared to accept that there should be at least a small number of other life forms out there like us.
The problem, as Enrico Fermi pointed out in the subsequent Fermi Paradox, is that if there are a considerable number of intelligent extrasolar civilizations out there among the stars, we should have started to see them by now, even with our relatively primitive telescopes and listening devices.
We measure the progress of human technology in years and decades: even though space travel has stagnated somewhat since the heady days of the 1970s, remember that in the last century the frontier of human technological achievement has moved from the hot air balloon to the interplanetary space probe.
Astronomers measure time across the galaxy in millions of years, not mere years, so assuming that our rate of progress is common to intelligent civilizations, there ought to be at least a few out there which are incredibly advanced compared to us.
This ought to make their wide-ranging interstellar activities even more visible to us. If you would logically expect to see evidence of life and instead see no such evidence, it is tempting to conclude that there for some reason there may not be life out there after all.
Thus, there are two basic alternatives. One is that extrasolar entities exist, but in forms so advanced that we cannot see them and are not yet capable of interacting with them.
Listening for radio transmissions implies that extrasolar entities must be using high-powered radios to communicate over large distances - but perhaps they are using some other system, or perhaps, for various reasons, they do not do much long-distance communicating. The alternative is both a chilling and exciting one: perhaps we are indeed (at least for the moment) the only intelligent life forms in this galaxy.