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Acoustic resonances in open systems, which are usually associated with resonant modes characterized by complex eigenfrequencies, play a fundamental role in manipulating acoustic wave radiation and propagation. Notably, they are accompanied by considerable field enhancement, boosting interactions between waves and matter, and leading to various exciting applications. In the past two decades, acoustic metamaterials have enabled a high degree of control over tailoring acoustic resonances over a range of frequencies. Here, we provide an overview of recent advances in the area of acoustic resonances in non-Hermitian open systems, including Helmholtz resonators, metamaterials and metasurfaces, and discuss their applications in various acoustic devices, including sound absorbers, acoustic sources, vortex beam generation and imaging. We also discuss bound states in the continuum and their applications in boosting acoustic wave–matter interactions, active phononics and non-Hermitian acoustic resonances, including phononic topological insulators and the acoustic skin effect.