What a fantastic question! To which there is still no definitive answer, but maybe I can point you to some research and thought experiments. This is certainly a question that astrophysicists have been pondering for many years. The universe is huge and old, composed of many galaxies; Earth is just a blip in our own galaxy, known as the Milky Way.

It is estimated that 100 billion (that's 9 more zeros!) galaxies exist with even more stars. Our sun is just one of those stars.That's a lot of galaxies and a lot of stars. It seems plausible that somewhere in those galaxies there could be a solar system like ours with planets that orbit different stars (known as exoplanets). So life from outer space seems probabilistically possible, even in our own galaxy. This argument is known as the Drake equation, which just makes explicit a probability calculation of the number of active (i.e., not extinct), intelligent (i.e., have some form of "language"), and communicative (i.e.. looking for other active, intelligent civilizations). It looks like this The Drake equation is nice and all, but it doesn't tell us how to find the values of each variable, so we can't get a number out of this. Still, it makes you think of the vast possibility that other life forms could exist out there...

Scientists have found that the universe is pretty much made of the same elements you find on the periodic table (through very clever means of measurement, if I do say so myself). There is a particular combination of elements that is conducive to life. But is that something unique to Earth? This is a question that many scientists have asked themselves. There are quite a few things you need to be able to sustain life, of which I list a few to give you a taste:

1) Habitability
That is, you need to be at just the right distance from a "sun" (i.e., star). If you are too close, it's too hot; likewise, too far, and it's too cold. Additionally, you want your planet to be able to rotate on its own axis (i.e., have day and night cycles), so that one side is not left hot and other col. This is especially important with respect to water. Keeping water in its liquid state is essential for all kinds of biological functions, and by extension life itself. Too hot, and it vaporizes; too cold, and it freezes.

This is also true about the distance with respect to the center of the galaxy you are in. For instance, in our Milky Way, the center is rife with supernovas (exploding stars) and a supermassive black hole that would kill all life with intense radiation.

You also don't want a star that is too big. These tend to be stars that have shorter life spans.

2) A bigger planet nearby
It turns out that because Jupiter is so big, it helps "absorb" many of the comets and asteroids that could otherwise hit Earth, which, as you may know from the dinosaurs, could wipe out quite of bit of life.

3) A large enough planet
Primarily, you have enough gravitational pull to sustain an atmosphere, though there may be other reasons.

4) A planet with plate tectonics
The Earth's crust (i.e., surface layer) is composed of many plates. The motion of these plates recycles carbon, which is the backbone of nearly all organic matter. This helps maintain the levels of carbon dioxide levels (CO₂) at a level habitable life.

There is even discussion of colonizing Mars so that does become habitable. This would entail getting and maintaining levels of CO₂ needed to warm up the planet, putting in some organisms that produce oxygen that will eventually lead to more complex forms of life. This is actually how life on earth developed (in a very simplified and curt manner). (And another interesting tidbit, it is the release of too much CO₂ in our own atmosphere that has been at the center of the climate change debate, but that is another story for another time.)

This actually leads me to an interesting point. Perhaps the image of Aliens you have is that from science fiction- ones that look humanoid with big eyes and are green. Although finding another civilization in outer space would revolutionize what we know of the universe, finding even simple organisms like bacteria would be monumental. There are several planets that have been identified as potential places that could have sustained life at some point- some in our own solar system (e.g., Europa, one of Jupiter's moons, and Mars) and many outside, such as Kepler-186f That is the conditions have been found that could have at one point sustained life. So there are lots of places that meet conditions to sustain life, but so far no dice. But with so many requirements, it really makes you wonder at how amazing it is that life exists here...

So perhaps there is life out there, we just haven't found it and perhaps they have not found us either. Or perhaps, we communicate differently and missed each other. Or maybe they are so advanced, they think us too primitive. Conversely, we may be too advanced for their form of communication. I think my favorite analogy is communicating to aliens may be like us communicating with ants (or vice versa). While we have spoken/written language, ants communicate primarily through pheromones (chemicals secreted into the air), which we have very poor receptors for! What do you think?

If you are especially interested in astrophysics, I recommend watching Cosmos with both Carl Sagan and then more recently with Neil deGrasse Tyson. They are really quite rewarding.

Hope this helps!
Best,