Additive manufacturing is a rapid manufacturing based on discrete accumulation to achieve prototypes or parts of products. Inorganic non-metallic materials, as one of the three major materials, have incomparable application prospect in medical, aerospace, automotive, construction, arts and crafts, as well as many other fields. In order to rapidly create devices with arbitrarily complex shapes, additive manufacturing of inorganic non-metallic materials is becoming a hot spot of current research. In view of the technical types, materials and other aspects, this article introduced research status and development of additive manufacturing in inorganic non-metallic materials at home and abroad. Several common inorganic non-metallic materials are compared and analyzed, such as Al2O3, Si3N4 SiO2, ZrO2, etc. The forming characteristics and the problems of several popular ceramic materials and sand–casting materials are illustrated with emphases. The key problems existed in additive manufacturing forming process of inorganic non-metallic material are pointed out and urgent to be solved at present. Furthermore, the impacts of the material handling process, three dimensional printing (3DP), Selective Laser Sintering(SLS), Selective Laser Melting (SLM) three-dimensional forming processes and post treatment process on the quality and performance of the forming parts are analyzed. Finally, the prospects in SLS of the gem material are put forward.