Acoustic metamaterials have expanded the capabilities of acoustic wave manipulation with diverse application potentials, such as negative refraction, superresolution, cloaking, enhanced absorption, nonreciprocity, active control, and material tunability. Acoustic metamaterials are also expected to affect ultrasonic acoustics, where countless applications, such as medical imagining, lie detection. Owing to the simplicity of the fabrication process—compared to those for electronic and display devices, for example, the acoustic metadevices may be commercialized, targeting old challenges such as noise abatement and selective perception in human audition. Moreover, many of the novel acoustic metamaterial structures have transcended the original definition of metamaterials as arising from the collective manifestations of constituent resonating units, but they continue to extend wave manipulation functionalities beyond those found in nature. The new ideas hatched in acoustic metamaterials research, coupled with the expanding technologies of computational simulation and additive manufacturing, will produce the next generation of acoustical materials and metadevices. This chapter will review the development of acoustic metamaterials from the initial findings of mass density and bulk modulus frequency dispersions in locally resonant structures to the diverse functionalities afforded by the perspective of negative constitutive parameter values and their implications for acoustic wave behaviors, including compact phase manipulation structures, superabsorption, and actively controllable metamaterials as well as the new directions on acoustic wave transport in moving fluid, elastic, and mechanical metamaterials, graphene-inspired metamaterials, and structures whose characteristics are best delineated by non-Hermitian Hamiltonians.