A corneal implant (50,60) comprising a body having a protruding center optic (52,62) at least partially surrounded by a rim (54,64), said body composed of a material having a tensile strength in the range from 0.1 MPa to 4 MPa and a modulus in the range from 0.1 MPa to 5 MPa, wherein center optic (52) can extend anteriorly from the rim (54) or the center optic (62) can additionally extend posteriorly from the implant.