Ceramics, with its excellent thermal, physical and chemical properties, have great potential applications in various fields, such as aerospace, energy, environmental protection and bio-medicine. With the development of relevant technology in these fields, the structural design of core components is increasingly complex, and the internal microstructures gradually become customized and gradient. However, the hard and brittle features of ceramics make it difficult to realize the forming of special-shaped parts by traditional manufacturing methods, which in turn limits further application. As a rapidly developing additive manufacturing technology, laser additive manufacturing technology presents a momentous advantage in the manufacturing process of extremely precision ceramic components: free molding without mold and support, quick response feature and short developing cycle, etc. At the same time, the technology can realize the flexible deployment of ceramic parts, which is expected to solve the problems mentioned above. Three kinds of powder-based laser additive manufacturing techniques of ceramic were reviewed in this paper: selective laser sintering and selective laser melting based on powder bed fusion technology; laser engineered net shaping based on direct energy deposition technology. The forming principle and characteristics were mainly discussed; the research progress of ceramic green body densification process in selective laser sintering technology and the forming principle, propagation mechanism and control methods of ceramic green body cracks in selective laser melting, and laser engineered net shaping technology were reviewed; the technical characteristics of selective laser sintering, selective laser melting and laser engineered net shaping technologies in shaping of ceramic parts were compared and analyzed; and the future development trends of laser additive manufacturing technology of ceramic parts were prospected.