Medical science has no way to transplant whole eyes. Our eyes are connected to the brain by the optic nerve.
Much like a fiber optic cable, the optic nerve is made up of more than one million tiny nerve fibers. This nerve cannot be reconnected once it has been severed. Because of this, the eye is never removed from its socket during surgery.
The cornea, the clear front part of the eye, has been successfully transplanted for many years. Corneal transplant is sometimes confused with an eye transplant.