A common feature that we consider to be alien is the eyestalk and rightfully so. To my knowledge the only vertebrate that even comes close to having eyestalks is the hammer head shark (if you can even call them stalks). Sure, many species of insects have evolved eyestalks, but they are unlikely to evolve the sapience needed for advancement.
So, what evolutionary benefits would an animal with eyestalks enjoy? Why would they evolve them in the first place?
Eye stalks have sort of happened in the past with vertebres. Mudskippers, rays, Crocodilians, even Frogs all have eyes that at least partially represent eyestalks. While these are more raised eyesockets than full on stalks, it can be usefull to talk about why these animals have these elevated sockets in the first place, and if it could be useful for them to be even higher.
Amphibians often have raised eyesockets when they spend a lot of time partially submerged or at the surface of the water. They have raised eyesockets both for protection from above water predators and to catch surface and above water prey.
Crocodilians and similar animals use their "stalks" in order to catch prey.
Fish, like rays, have raised sockets in order to survey the area while submerged under sand or other ground debree. Mudskippers similarly use these stalks to see above the mud.
Looking at these examples it appears that "raised eyes" among vertebrates relies on the need to see above a visually obscured medium (ie water, mud, sand etc...).
But what stops them from growing stalks further? Simplicity is one, if stalks don't need to be higher, then they won't get higher. Another, as others have commented, is a risk to vulnerability.
But shouldn't even slightly higher "stalks" be better for even deeper camoflauge on say sturdier animals like crocodilians? In crocodilians, they not only have raised eyestalks, but raised nostrils Raising eyestalks would mean possibly loosing hydrodynamic efficiency in water locomotion, as the nostrils would also need to be raised, possibly for little benefit. Nonetheless, it is a viable option of such camoflauge would bee needed.
Now at this point, you may be asking why I left an obvious example out. The Hippopotamus. Out of all these animals, this extinct species of Hippopotamus actually did have quite close to actual eyestalk eyes.
Now the hippo itself already has raised sockets, and follows the previous reasoning presented for needing them (needing to see something above a medium [water]). But this species was special in that they were pretty close to actual stalks, not just slightly raised. I can't comment to why this evolved specifically, but I suspect that because the hippopotamus's nostrils are so far raised in the first place was at least what enabled such a evolutionary trait to not not carry the negatives you might see with modern crocodilians. The nostril height itself was spurred from the extra space needed for the massive canine tusks hippos sport.
If your species needed to see above an obscured surface that was not totally opaque (like water) and wouldn't lose out on another trait massively because of elevated eye-sockets, and also needed to be camouflaged by the surface, then eyestalks would be very beneficial.
From a strictly terrestrial biology viewpoint, I am unaware of any 'higher' species that have evolved 'eyestalks'. With the same observation however is the correlation of eye type and complexity to the complexity of animal.
I have only been able to locate eyestalks in invertebrates, specifically in mollusks, and some arthropods.
I think that there is reason to believe that an enhanced 360 view would provide some advantages on the evolutionary path, but appears to be out weighed ( at least on Earth) by the need to protect complex eye structures.
Eyes are among natures most diverse sensory organs, from basic photosensors to a raptors amazing vision, to compound organs such as bees have.
The correlation between complexity of eye structure, the specialization of the eye for a species, and the need to protect the organ in a bony cover or socket lead me to feel the primary advantages would be in enhanced field of view, most likely in simpler 'prey' animals.
Purely speculation and opinion...
Eyestalks allow wider vision without complicating the eye. Imagine the ability to look behind without turning your head. Being able to see two different locations would also be considered as a bonus.
But these types of eyes are vulnerable. If a creature is already weak and cannot risk physical damage, eyestalks may not be the weakest point. But in vertebrates, especially in mammals, the body is not very vulnerable, it can take a beating and still survive. If your aliens are physically weak (not necessarily in comparison to humans), having eyestalks might give them an edge for survival.
Considering the skull contortions of a flounder to move both eyes to the same side of the head, the nose of cetations moving to the back of the head, and the eyes of the hammerhead shark, it is reasonable to suppose that eyes could be raised up as a periscope, or moved far apart to give an enhanced paralex.
Allowing the structure that supports the eyes to then develop a degree of movement is a separate step. Speculate here: consider how the trunk of an elephant is formed from a fusion of the upper lip and the nose. The star-nosed mole develops the eponomous organ from tissue of the cheeks and face.
So it is conceivable that the needed structures could grow from the head and face area. If the original “extension” was not bone but lightweight cartilage like the nose and ear, it might easily become flexible, and formed by fusing cheek and ear tissue. Muscles adapt to move it.
With the exception of the stalk-eyed fly, most animals with eye stalks lack an effective way of looking around without them. Snails and slugs are slow-moving and it costs them a lot of energy to turn their head around, while crabs and the extinct trilobites are completely unable to turn their 'head' at all. For species such as this, having eyes that can look in any direction is beneficial. For most vertebrates, being able to turn the entire head around is pretty easy, so it makes more sense to keep the eyes fixed in the skull where they are well-protected.
That doesn't mean it can't happen, though. Frogs, which have rigid necks and can't turn their heads, might benefit from eye stalks, although these might be vulnerable when they jump. In fact, their bulging eyes might be a compromise solution. And speaking of frogs, any species that lived in marshy regions and hid from prey in murky water could benefit from eyes that could keep watch like a periscope.
And in a pinch, just look at the stalk-eyed fly. Their eye stalks don't seem to help them at all, and are considered to be a classic example of runaway sexual selection. That could potentially occur in any species for no real reason at all - if that's the route you want to go, of course, long eye stalks should be considered attractive to members of the species.
The mudskipper fish is the nearest thing to a vertebrate with eyestalks that I can think of. If mudskippers took to burying themselves in deep mud, their eyes might need to be raised up a bit more to poke out of the mud. But I suspect they'd solve the problem by positioning of their body, rather than evolving their eyes.
To get eyestalks like stalk eyed-fly or a ghost crab will take a phenomenal amount of re-engineering of a land vertebrate's skull. Basically you are going to have to turn a socket designed to be tucked away for protection into something sticking out into danger. Crustaceans protect their eyes by folding them sideways into slots in their carapace. I suppose a reptile with an incredibly kinetic skull (lots of articulation points within it), such as a snake might have the basic toolkit to create a hinge joint or retracting mechanism to pull the eyes into safety.
Of course you can't see properly with retracted eyes, which makes them a bit like Joo Janta Peril Sensitive Sunglasses! :-)
I saw a swamp fish in Guatemala that seems to have 4 eyes - two for below water vision, and two on stalks for above water vision. It appears that as they swim around, their stalk eyes watch for predators from the air. (Wikipedia telles me that they are called Anableps Anableps and they a only have two eyes. The locals call them "cuatro ojos" though.)
I think any species that need visual information from two different environments has a good reason to evolve eye stalks - whether to avoid predators, whether to detect pray, or maybe to gather information about nature for survival.
Why do they need separate eyes? The same reason we need goggles to see underwater: Because the index of refraction of water is different than air, so having a set of eyes that is adapted to water and another set adapted to air is understandable.
In the case of fish, they can't survive for very long in the air, but information from air is very helpful for survival.
The index of refraction changes between materials, and it even changes between temperatures of gas. So perhaps they have strong temperature gradients in their atmosphere, so having eyes on stalks or tentacles would be highly favored in all species.
Eyestalks give 'a better field of vision' to the animal. They may have an improvement that benefits their likelihood of surviving, thermal-vision and ability to see from long-distances. They may have a better chance of finding food, water and a mate.
Eyestalks could be used to have a wider FOV, but they will most likely never appear on a sapient species because
All of these drawbacks make it simply not worth it for the single benefit of an increased FOV, especially considering that it's not a continuous augmentation of the visual field, when it's so much easier to just move your head/body.
Eye stalks may be a more of a benefit in a swampy/marshy region. It is also possible that an invertebrate species develops intelligence (many sci-fi universes have intelligent insects, the Tholians from Star Trek come to mind)
My first consideration is an alligator, that pops only its eyes and nose out of the water. the stalks would give them a few benefits like being able to see in a few directions, but if a bird checked out its eyes and tried to poke them out or something, the could be retraced. they could also be like lures catch birds or something like that.
Given that intelligent life on earth evolved after a group of ape-like ancestors were forced out of forested areas onto the plains of Africa, I will allow that some of the alligator like eye-stalk creatures (I'll call them alescs for short) are smart enough to notice some overcrowding and decide to move out of the swamp and onto a plains or forrest environment. they don't have much of an advantage here, so they use and develop intelligence here, in a new environment, and start using tools.
Some fish larvae do have eyestalks. This is known as the stylophthalmine trait, and has evolved at least 4 times. However, this trait generally involves bulbous elliptical eyes, which may be hard to support on nekton or terrestrial creatures
It already has.
Hammerhead sharks have very peculiar-shaped heads that some might describe as eye stalks.
And it is possible that it has occured in prehistoric times as well.
Perhaps the strangest prehistoric animal is Tullimonstrum, otherwise known as the "Tully monster." This bizarre animal's taxonomy is almost completely a mystery. Nothing has been positively determined beyond the clade bilateria, which includes all bilaterally symmetrical animals.
Some scientists think that it was an arthropod, some think a mollusk, others think a vertebrate.
Here's what this creature looks like:
https://www.researchgate.net/publication/298434474
https://www.livescience.com/ancient-tully-monster-vertebrate.html
Sure many species of insect have evolved eyestalks, but they are unlikely to evolve the sapience needed for advancement.I think the same would apply to vertebrates, for some given values of sapience. At least I think these guys are vertebrates. $\endgroup$