Abstract: Phononic crystals and acoustic metamaterials have extended the elastic properties of acoustic materials in the natural world. This kind of artificial composite material, due to local Mie resonance and Bragg scattering of the periodic structure, exhibits exotic dispersion characteristics, which leads to negative effective elastic parameters in certain frequency ranges; this gives rise to many fascinating acoustic effects, such as phononic band gaps, negative refraction, superprisms, superlenses, hyperlenses, extraordinary transmission, and extraordinary sound shielding. In the meantime, a type of acoustic surface evanescent wave with subwavelength characteristics on the surface of phononic crystals and acoustic metamaterials has attracted new attention, and research on its excitation, propagation and coupling is very important for understanding the physical essence of the novel propagation effects in these materials. As a new class of artificial acoustic medium, they should provide plentiful potential applications in acoustic isolation, vibration control, heat manipulation, and the development of new acoustic devices. This paper will review the research on phononic crystals and acoustic metamaterials over the last ten years, and discuss possible future developments.