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?