Yes, fish do sleep and they do this with their eyes open simply because they have no eyelids. Aside from this, a fish's eye works in exactly the same way as for other animals i.e. has a contractible iris, a pupil to allow light to enter the eyeball etc. However, a fish's cornea has no function as a lens; the refractive index is too similar to that of water. Instead, the lens itself, has a high refractive index and functions as the single focusing element of the eye. Unlike the lens in a human eye, a fishes lens is spherical and cannot flex to focus. Instead the lens moves closer or further from the retina in a similar manner to a camera lens.

As fish do not have necks, they cannot turn their head to look in different directions. To compensate for this, their eyes have a wide field of view. Depending on the placement of the eye, some fish, particularly those that are preyed on, have 360 degree vision.

Fish can recognise colours and patterns. This is most obvious in the cichlid world where colours and patterns are used to communicate, identify species (for defence of the brood), to indicate breeding status and for camouflage.

The size of the eye depends largely on environmental or behavioral conditions. If the fish is active at night, lives in murky waters or is usually considered as prey the eyes will tend to be larger.