Previously, I have shown the possibility for aliens to exist from a probability perspective, arguing from the abundance of chances in the universe. 
I also showed how it is entirely possible for intelligent life to exist outside Earth, even in light of philosophical and religious considerations.  But now I want to take a while to throw UFO sightings out the window and think about what alien life could look like, what kind of biology and chemistry it might make use of and where it could physically thrive.
Regarding life which we can observe on Earth there is much diversity.  Many species of fish and all sorts of microbes and fungi would startle anyone at first sight. 
The diversity amongst living creatures on our own planet, all derived from the same evolutionary stock and physical environment, goes to show how diverse life forms in general could be. 
Carl Sagan gets to this in his book “Cosmos” where he says, “Were the Earth to be started over again with all its physical features identical, it is extremely unlikely that anything closely resembling a human being would ever again emerge. There is a powerful random character to the evolutionary process.  A cosmic ray striking a different gene, producing a different mutation, can have small consequences early but profound consequences late… On another planet, with a different sequence of random processes to make hereditary diversity and a different environment to select particular combinations of genes, the chances of finding beings who are physically similar to us is, I believe, near zero.”
Now let us take into consideration chemical and biological factors with other life forms. 
It is very likely for water to be a key substance in any life-form, because it is abundant and because it has very useful chemical properties.
But because of water’s freezing and boiling point, there are many locations where water-based life would not survive. 
Just look at our own solar system. Water freezes on Mars because it is too far away and the atmosphere is too small to have substantial greenhouse heating effects; therefore, most water based life would probably simply freeze immediately.  Water boils at 100 degrees Celsius, so life would stand no chance on Mercury or Venus which are both hotter than boiling because of their proximity and Venus’s massive greenhouse warming effect. 
What about beyond Mars?  Well according to Neil DeGrasse Tyson in his book “Space Chronicles,” evidence for life might be found “beneath the dried riverbeds of Mars (where there may be fossil evidence of life that thrived when waters formerly thawed) and the subsurface oceans that are theorized to exist under the frozen layers of Jupiter’s moon Europa, whose interior is kept warm by gravitational stresses from the Jovian system.  Once again, the promise of liquid water leads our search.”
Besides just water, there are only a few chemicals which life on Earth utilizes, and they happen to be the most abundant in the universe. 
Neil DeGrasse Tyson makes an appeal to chemistry, “Aliens need not look like us to resemble us in more fundamental ways … you can bet that if life is found on another planet, it will be made of a similar mix of elements.”
Therefore, it is not unlikely for other life to probably follow a similar chemical pattern, even if perhaps carbon is replaced with silicon or probably DNA will be replaced with some other efficient, chemical, data storage mechanism. 
We have a good idea of what the biology and chemistry will be like. Our version of biology is probably rather normal in the grand scheme of things, but there is always the chance for a total surprise.
An original attempt at alien structure and biology comes from Arthur C. Clarke’s (no relation) science fiction story, “Rendezvous with Rama.” 
In the book a scouting mission goes to explore a large spaceship-capsule which contains at first glance nothing at all, but as the capsule approaches the Sun and gets progressively warmer inside, an automated life system kicks in.
Toward the end of the scouting mission, many different life forms begin to spawn out of the system and they are investigated. 
First this comment is made, “We have a complete record of terrestrial zoology, and we find in it one strikingly parallel with Rama,” but elsewhere this observation about the alien zoology is made, “I would say that they are robots, biological robots – something that has no analogy on Earth.” 
Clarke finishes his fictitious and very creative account of the physiology of the aliens encountered on the capsule Rama by describing the intelligent masters responsible for the ship.
They have a very narrow central “waist, thorax, or some division unknown to terrestrial zoology” which then tapers to a meter in diameter section with three limbs coming out. 
Clarke’s Raman’s with their triplicate limb structure and highly robotized and hive-mind radio communication, are just one genuine attempt to describe possible alien life. 
Basically we should not expect any aliens to closely resemble us, but we can probably make a few assumptions about their chemistry, if not their biology.
Finally, I would like to quote Tyson again: “The discovery of extraterrestrial intelligence, if and when it happens, will impart a change in human self-perception that may be impossible to anticipate.” 
I hope we gain a cosmic perspective which shifts humanity’s focus away from our current petty arguments and toward survival as a whole in the vast and likely dangerous universe.