Abstract:Acoustic metamaterials are a special type of man-made composite materials that are characterized in the framework of continuum medium theory.They obtain anomalous dynamic material properties, such as negative dynamic mass, negative dynamic modulus, negative refraction, by careful designs of micro-scale structures.The metamaterial concept brings us the opportunity of wave propagation control, as make metamaterials potentially applied in practical engineering.This review paper aims at explaining the concept of microstructure design of elastic and acoustic metamaterials, acoustic metasurfaces, and active metamaterials, as well as the relevant research advances.The generalized concept may be of benefit to the design and material realization of wave control structures.