Having a second eye allows a creature to perceive depth and to focus easily on its prey, so are there any sound theories for how would Cyclops in Greek mythology go hunting using only a single eye? Or this is the reason they aren't here anymore?
In addition to Isaac Kotlicky's answer, a quick movement of the head would give the cyclops a different angle of view, and by comparing the apparent shift of the target (the "parallax"), the cyclops could gauge the distance in a manner similar to binocular vision.
I've seen my cats do this when preparing to jump up to something, I think to get a better idea of the distance for the jump. They already have binocular vision, but bobbing their head gives them a better baseline.
Cyclopes herded giant sheep and therefore did not need to hunt wild animals. Besides, ordinary-sized animals would only be a bite or two for one of the giants, so why even take the trouble to hunt them?
Depth for humans (and most animals) is figured out by sampling different overlapping images at a defined spacing (ocular distance) and interpolating depth by the shifting of objects within those two images. Some animals (such as horses, rabbits, chameleons, and many birds) have little to no real overlap in their visual fields. So depth perception isn't a necessity for survival, but it is helpful. In our case, the size of the cyclops means that it has no natural predators, and that it can easily outrun prey.
Just because it has a single eye doesn't mean it can't have depth perception, it just makes the process more difficult. The lens on your eye is constructed to focus light on the retina in the back of the eye, and especially on the fovea, the part that senses the most detail. What if it weren't? Let's assume that the lens, rather than focusing, split the light into two images focused on different parts of an expanded retina. Instead of depth interpolated through the angular depth caused by the distance between the eyes, it would be caused by the angular deviance between the two samples. To humans, this would look like a distorted fun house mirror. To a cyclops so evolved, they would have depth perception.
I would say one of two things would allow it to hunt. One would be moving the head to get 'binocular' vision. You see this in pigeons and chickens etc. These birds have eyes on the side of their head to maximize their field of vision. As they walk they their heads bob back and forth, it looks funny but it gives them to snap shots close together giving them some depth perception.
The other would be the eye produces a laser, which would act like sonar, bouncing a beam off items to measure their distance. This would even allow them to see fine in perfect dark. (this is an idea from David Brin's uplift series)
One translation of the Odyssey insisted that the proper translation was something like "Goggle eyes", and there is a tradition in the region that cannibals live in the wilds but have a third eye in the back of their heads, which may be what was being referred to when Odysseus and his crew drove a stake into the eye of Polyphemus.