This paper first reviews the research progress of carbon fiber-reinforced sandwich plates with grid cores, truss cores, and foam cores, and the results can be summarized in the following four points. 1) The load-bearing capacity and energy absorption capacity of grid-core and foam-core structures under bending loads have been improved by toughening with short fibers and Z-pinned fibers. 2) The progressive buckling mode of the core layer under compressive loading can significantly improve the energy absorption capacity of a sandwich structure. 3) The compressive failure of a truss-core sandwich structure is closely related to the strength at the nodes. 4) Following a literature review, this paper discusses the existing problems in sandwich structures and the corresponding countermeasures, and the results can be summarized in the following two points. 1) After implementing the current toughening measures, the debonding is improved to a certain extent; however, this approach does not prevent debonding. 2) No method has been presented that can increase the strength of the end nodes in truss-core members. Therefore, it is encouraging that a trabeculae/honeycomb-core sandwich structure composed of fiber-reinforced proteins—mimicking the biological structure found in a beetle forewing—can effectively solve the abovementioned problems.