Sand erosion has always been a key threat to the performance and service life of aero-engines. The compressor, the key component installed at the front of the aero-engine, suffers the most from sand erosion, especially compressors serving in deserts. Ceramic hard coating is a traditional way to improve the hardness and wear resistance of cutting and grinding tools. It may also be used to improve the erosion resistance of aero- engine compressor. However, the mechanism of erosion damage is complicated, which may include wear, secondary erosion, anisotropic erosion, impact, and fatigue. Recent research discovered the major problems with ceramic hard coating on aero-engine compressors. In this paper, these following problems are discussed: the design of coating material and structure, the preparation method and technology, the effects of droplets and clusters of coating surface, microstructure and characteristics of interface. The review of the major problems and possible solutions discussed in this paper may contribute to the future research on erosion coating theoretically and practically.