Vision loss can occur when the cornea loses transparency or changes shape. The most effective treatment to restore vision is to use full or partial layers of donor cornea for corneal transplantation. However, there is a severe shortage of donor corneas worldwide, with more than 98.5% of patients with corneal blindness waiting for donor corneas. In addition, there exist some problems such as the possibility of infection, allotransplantation immunologic rejection, and other problems after corneal transplantation. Therefore, tissue-engineering corneas have been widely studied over the years as a viable alternative to donor corneas, with different materials and methods. And in nearly ten years, the research has had breakthrough progress. The ultimate goal of the research is to construct a full or partial tissue-engineering graft with good transparency, biocompatibility, and appropriate mechanical strength to repair, regenerate, or replace diseased corneas. This review discusses the research progress and existing problems about the most frequently studied natural biomaterials in recent years. These biomaterials include amniotic membrane, acellular cornea, collagen, and silk. In addition to the future research directions, other challenges related to the biomaterials discussed in this field are illustrated.