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Acoustic metamaterials (AMs), which are materials composed of subwavelength periodic artificial structures with specific designs, have drawn significant research attention. This is because of the extraordinary abilities of AMs to manipulate acoustic waves compared with those of traditional acoustic materials. In this review, current advances in AM research are comprehensively investigated and summarized. First, major theories regarding AMs, including the acoustic wave equation, crystal lattice and energy band theory, effective medium theory, and general Snell's law, are explained in detail. Existing AM structures are then described and divided into several categories based on their structural characteristics and responses to acoustic waves. Furthermore, to bridge the gap between design and practical application, both conventional and advanced AM manufacturing methods are summarized. The applications of AMs in the fields of acoustic cloaking, acoustic lensing, acoustic absorption, noise reduction, and supernormal sound transmission are particularly delineated. Finally, contemporary challenges, trends, and strategies relevant to AMs are discussed. This review aims to provide a comprehensive collection of AM‐related knowledge, including information regarding physical theories, structures, fabrication approaches, and applications, which will help promote the further development of AMs.

Auxetic mechanical metamaterials (AMMs), as an exciting paradigm of metamaterials, have attracted increasing attention due to their interesting mechanical properties (e.g. negative Poisson's ratio), as well as the emergence of advanced manufacturing technology (e.g. 3D printing). Although various reviews on AMMs, their structures, properties, and applications, have existed, it still lacks a comprehensive review in terms of manufacturing methods. Herein, the latest progress in AMMs is extensively reviewed, including AMMs' structures, characteristics, manufacturing methods, and applications. In addition, the current challenges and future works of AMMs are concluded and discussed. This Review aims to serve as a collection of knowledge that supplies more comprehensive understanding and inspiration to support further developments of AMMs from the perspective of design and manufacturing.

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