This paper aims to give a review of our knowledge on the human cornea, its structure, and its behavior, for mechanical modeling. It presents first the general organization of the cornea, as well as its macro and microstructures. In a second time, we detail the Optical Coherence Tomography (OCT) techniques, which are used in clinics and in research to observe the cornea. Then, we present the experimental characterization of the cornea mechanical properties. Finally, we review the modeling approaches that have been used to describe the elastic response of the tissue.