With the development of science and technology and industry, people’s requirements for the characteristics of crystals and ceramic materials are getting higher and higher, and the requirements for materials are also getting higher and higher. People are no longer satisfied with the characteristics of cubic crystal systems, and are also interested in the characteristics of various other crystal systems. At the same time, people are no longer satisfied with the inherent characteristics of single-component materials. Multi-component crystals can integrate the advantages of each component material, and the fusion of each component material can obtain some new characteristics and receive a lot of research. Studying the physical characteristics of crystals and guiding the corresponding design has always been a rapidly developing field with application prospects. This chapter studies the nonlinear acoustic propagation characteristics and acoustic memory phenomena of sound waves in various crystal systems and ceramic materials.