A display system can include a head-mounted display configured to project light to an eye of a user to display virtual image content at different amounts of divergence and collimation. The display system can include an inward-facing imaging system possibly comprising a plurality of cameras that image the user's eye and glints thereon, and processing electronics that are in communication with the inward-facing imaging system and that are configured to obtain an estimate of a center of cornea of the user's eye using data derived from the glint images. The display system may use spherical and aspheric cornea models to estimate a location of the corneal center of the user's eye.