Corneal transplantation remains the ultimate treatment option for advanced stromal and endothelial disorders. Corneal tissue engineering has gained increasing interest in recent years, as it can bypass many complications of conventional corneal transplantation. The human cornea is an ideal organ for tissue engineering, as it is avascular and immune-privileged. Mimicking the complex mechanical properties, the surface curvature, and stromal cytoarchitecure of the in vivo corneal tissue remains a great challenge for tissue engineering approaches. For this reason, automated biofabrication strategies, such as bioprinting, may offer additional spatial control during the manufacturing process to generate full-thickness cell-laden 3D corneal constructs. In this review, we discuss recent advances in bioprinting and biomaterials used for in vitro and ex vivo corneal tissue engineering, corneal cell-biomaterial interactions after bioprinting, and future directions of corneal bioprinting aiming at engineering a full-thickness human cornea in the lab.