This chapter introduces the fundamental principles, historical evolution, and current research frontiers of acoustic metamaterials and metasurfaces. Acoustic metamaterials, comprising subwavelength artificial structures, enable unprecedented sound manipulation by achieving exotic properties like negative mass density and elastic modulus. Key developments include pioneering designs such as localized resonant sonic crystals, Helmholtz resonators, and coiling-up space structures, which facilitate phenomena including negative refraction and tunneling. Acoustic metasurfaces leverage phase modulation across ultrathin planar structures for wavefront control under the generalized Snell’s law. The chapter further explores specialized branches: acoustic one-way transmission (breaking reciprocity via nonlinearity, airflow, or circuits), acoustic asymmetric transmission (achieved through asymmetric linear structures without violating reciprocity), and acoustic focusing (enabling compact, efficient lenses using gradient-index metamaterials or metasurfaces). Current challenges and future trajectories focus on active, multifunctional, and three-dimensional systems for applications in medical ultrasound, sound communication, architectural acoustics, and noise control.