There is actually a meaningful chance that alien civilizations - provided such exist within range - may be detected in the foreseeable future, and the way it may happen has nothing to do with the sort of First Contact fantasies we often see in movies and TV shows. I will first discuss those highly improbable scenarios, and then describe a scenario that actually has the ring of truth and could happen in this century.
Fantasy Scenario 1: Aliens Arrive Unannounced.
This is a lot of fun to imagine, but it's simply not going to happen. Unless an advanced civilization lives within the 90-year light-sphere in which our activities are unambiguously detectable - or else just happens to stumble into that region, and is specifically looking for signs of technological activity - no one would know we exist. The atmospheric signs of biology, however, have been in place for a few billion years, so the biological light-sphere encompasses a significant portion of the known universe. We can reasonably conclude from this either that biology as we know it is not terribly interesting to civilizations with interstellar transport capabilities; that civilizations are aware of our planet's biosphere and have found no reason to visit; that no civilizations who have detected biology in this neighborhood have transportation technology capable of traveling the distances involved; that terrestrial biology has simply not been detected; or, very unlikely, that no one is out there.
It is plausible that biochemistry occurring under conditions we're familiar with is not especially interesting over unknown processes in more exotic media. The true definition of "life" may be far broader than we can currently articulate, and life processes as we know them may be only the tiniest sliver of a vast spectrum. The complexities of organic chemistry on Earth may not be mysterious or intriguing at all to a civilization with a broader perception of that spectrum, and thus there would not be any particular motive of curiosity to come here. Or else it may be so commonplace that it's nothing more than a footnote in some catalog. "Oh, look, another planet with liquid water-based carbon chemistry. Ho-hum. No need to spend on any time investigating that further."
The greatest strike against this scenario, in my opinion, is simply the speed of light: Yes, there are theories implying the possibility of superluminal travel, but none of them that place the energy involved within reach of a remotely comprehensible civilization have been confirmed. In fact, we are not even at the point where we can articulate practical experiments that could do so. In other words, we have no rational reason to believe that advanced civilizations travel faster than light, and thus the default assumption must be that interstellar travel is subluminal and takes anywhere from centuries to millennia to move among a local group of a few dozen adjacent stars at maximum speed for a fusion or antimatter-driven spacecraft.
Beyond that local group, the proposition goes from dubious to preposterous - tens to hundreds of thousands of years on a one-way trip, even taking relativistic time dilation into account. Since, as noted above, the likelihood that human civilization has been detected is trivial, an ET intelligence would have to commit such time and resources to arriving at what might be a generic living planet, and whose surface conditions would change substantially multiple times en route. During this journey, they would have to first of all not all die, either in a major catastrophe or else through slow breakdown. In addition, they would have to remember where they're trying to go, and not either find some better target along the way or just settle for less rather than risk continuing. So in the unlikely event such a journey was undertaken, the likelihood of it arriving is even lower by far.
But perhaps the greatest strike against the scenario is a simple matter of relative technological difficulty - traveling for thousands of years is a much bigger and more profound undertaking than just building ecologically closed-loop cities on airless bodies or terraforming hostile planets with the potential to have natural ecosystems. There's just no economic basis for investing that level of effort to reach a habitable planet: By the time a civilization had the technology to do so, they would be more than capable of settling just about anywhere - asteroids, artificial stations, moons, hostile planets, it wouldn't matter. If they can survive for millennia in a spacecraft, no matter how large, then they have mastered closed-loop recycling of materials and food replication - which means they can get their raw materials from anywhere, anytime. The notion of a greedy, exploitive species coming here to steal the Earth's anything is a joke.
If we were to imagine that aliens in Independence Day actually existing, and for some bizarre reason coming to this solar system, they wouldn't bother with Earth. They would be out in the Oort cloud snatching up our comets and causing astrophysicists to scratch their heads at the odd gravitational perturbations on Kuiper Belt Objects their giant ships were causing - not blowing up the White House and the Empire State Building. But even that much is trivially unlikely. So, no alien visitations.
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Fantasy Scenario 2: Jodie Foster Hears a Who
The next most common fictional scenario is the detection of an alien beacon, as we saw in the book and movie Contact. This is somewhat more plausible than a visitation, but remains extremely unlikely for many reasons. First, as already noted, the human technological light-sphere is only about 90 light-years in radius, and even if we posited the compound improbabilities of (a)an advanced civilization being within that sphere at the present time, (b)being interested in detecting fledgling technological civilizations at this time, and (c)defining "fledgling" as being exactly at the level we are rather than something way ahead of our present capabilities, we would also have to imagine that they want to contact these youngsters the moment they're detected, and that's a whole lot of very unlikely suppositions in one scenario.
Firstly, technological civilizations are likely to be spread out not only in space, but in time, so the chances of one being close enough to both see us and open dialog in a meaningful timeframe is trivial. As a rule, most of the civilizations whose EM traffic would be detectable are already dead or have moved on to something much more exotic, since they would be thousands of light-years apart, so rationally there would not be a very significant purpose to communicating.
To get around this, we would have to imagine every nook and cranny of the galaxy being filled with automated detectors that trigger a message upon detection of technological activity. They would have to be absurdly sensitive, have absurdly powerful broadcast capabilities, and operate continuously without maintenance for millions of years. And even then, the vast, overwhelming majority of them would never see a damn thing. The bulk of the remainder would detect the flowering and then deaths of ephemeral civilizations, and perhaps have been the cause of such deaths in some cases. But basically, there is no rational reason to invest such resources on such a rare and transient phenomenon, even if one possessed the godlike technology. The case for killer-detectors that snuff out fledgling civilizations is even more dubious, given how few of them would likely survive even without interference.
Then there's the matter of when a civilization interested in contacting youngsters would deem it best to open up dialog, even assuming all the other improbabilities. We have to assume such people would be relatively careful about this, and invest some thought in it, so how likely is it that right now would be when they'd choose to send a message after detecting us? How long was the comparable period in their own history - they may have spent thousands of years gradually developing electronics and honing their mastery of information technology before they took another step and became what they consider "civilized." It's entirely probable that such a society would have some version of the Prime Directive guiding it not to disrupt natural progress by announcing themselves.
Even one of the above premises for this scenario is preposterous, but all of them put together make it only slightly more likely than alien visitation. So, basically, no alien signals. Not gonna happen. It's good that we tried SETI, and I support the goals, but the methods of seeking out ET were ill-conceived. We will not find aliens by trying to detect signals beamed at us. There are none. As much as anything can be stated in absolute terms, it's reasonable to say that.
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The Plausible Scenario: Long, Slow Accumulation of Telescopic Data about Extrasolar Planets
Right now we are in the early stages of discovering planets in the size range of Earth - i.e., big enough to hold on to an atmosphere, small enough that it has a solid surface in direct contact with that atmosphere (as opposed to being beneath a global supercritical ocean). The mass range involved is about Mars to roughly a few times that of Earth - rare conditions could make something above or below this range habitable, but they would be unlikely to occur on a consistent basis.
The next step after finding terrestrial-range planets is to discover which ones exist under potentially habitable conditions (as we know of them) - a consistent temperature range across much of the surface where liquid water can survive, and atmospheric pressures conducive to it. We already have discovered a few terrestrial-sized planets that orbit their stars in the so-called "habitable zone" - i.e., where the amount of sunlight reaching their vicinity is right for liquid water - but we don't yet know whether the atmospheric chemistry on those worlds is right for it. They may be like Venus or Mars rather than Earth - the water may all be in the atmosphere, or in a global ice shell. But sooner or later we'll find planets in Earth's size range that have the right temperature and pressure profile on their surfaces.
But even that isn't quite enough - a planet can have running water, calm weather, and consistently warm temperatures but be devoid of any but the most basic and relatively undetectable forms of life (e.g., subterranean anaerobic bacteria) if the atmosphere doesn't have the right chemistry for respiration. I don't know enough on the subject to speculate what kind of gas compositions could exist on an otherwise Earthlike world that might hinder life, but even on this planet the fluctuations in our atmosphere have had drastic consequences for biology in the past. So we have to scan terrestrial-sized planets in the habitable zone for atmospheric traces of biology (e.g., oxygen, methane, etc.) - something that will take a new generation of space telescopes beyond what we currently have.
And once we have the ability to look at atmospheric composition in detail, sooner or later I think we would run into some...anomalous...readings. Molecules in an atmosphere that we don't know of any natural process generating in any significant concentrations. Molecules that exist in our own atmosphere only because of technological activity. At first scientists would be very careful about dealing with such implications, and would conduct a thorough investigation for natural processes that might explain them. Most likely they would come up with something that could happen without technology to create those compounds, but over time more and more lines of evidence would converge - more anomalous readings, more passionate debates, and increasingly tenuous rationalizations for why the readings don't indicate technology. Such a process would probably take decades, as the legendarily stodgy community of planetary scientists begins to grudgingly concede that technology is the most likely explanation.
At first, as we could expect, there would be a lot of hyperventilation over this development - Aliens! A lot of nonsensical, ill-informed, and completely idiotic articles in the news media. A lot of ridiculous speculation by people who don't know what they're talking about: Starry-eyed nincompoops with Steven Spielberg fantasies, and snake-eyed paranoiacs retreating into their survivalist compounds awaiting the alien invasion, etc. etc. Since, statistically speaking, the planet in question would be thousands of light years away, no probes or communication of any kind would be practical, so the nonsense would slowly die down while scientists continued to accumulate telescopic data and draw ever-more-detailed inferences from it. We can bet, at least initially, that governments around the world would pour resources to advancing telescope technology in order to get more detailed readings on a wider range of instruments.
At some point, ever so slowly, we might advance telescope technology to the point of detecting artificial electromagnetic activity on that planet, and perhaps elsewhere in the same solar system, indicating space colonization. We could imagine vast arrays of networked telescopes spread across the entire breadth of our solar system and focused on the alien system - the technology already exists, but would be expensive without some overriding mission like the one being envisioned here. After decades of concerted effort, we might get blurry photographs of the planet, giving a vague sense of its coloration, some continental outlines, and how the clouds move. We might also be able to discern political (or at least economic) boundaries in the EM emission patterns.
But by the end of this century, we probably still wouldn't know what they look like, what they think about anything, the nature of their languages, their history, their evolution, their goals and aspirations, or whether they know we exist. The study of them would spawn an entirely new science, and keep us busy for centuries trying to squeeze every last bit of information out of the sketchy and limited data we manage to obtain. It would also radically accelerate efforts to find still more civilizations using the lessons we had learned improving our technology to study the first aliens we had detected. This is something that can happen - a future that can plausibly occur in the lifetimes of people alive today.