The ability to clearly observe one's environment in the visible spectrum provides a tremendous evolutionary advantage in most of the world's habitats. The complex optical processing system that has evolved in higher vertebrate animals gathers, focuses, detects, transduces, and interprets incoming visible light. The cornea resides at the front end of this imaging system, where it provides a clear optical aperture, substantial refractive power, and the structural stability required to protect the fragile intraocular components. Nature has resolved these simultaneous design requirements through an exceedingly clever manipulation of common extracellular-matrix structural materials (e.g., collagen and proteoglycans). In this review, we (a) examine the biophysical and optical roles of the cornea, (b) discuss increasingly popular approaches to altering its natural refractive properties with an emphasis on biomechanics, and (c) investigate the fast-rising science of corneal replacement via synthetic biomaterials. We close by considering relevant open problems that would benefit from the increased attention of bioengineers.