  Topological acoustics is an emerging field that lies at the intersection of
condensed matter physics, mechanical structural design and acoustics
engineering. It explores the design and construction of novel artificial
structures, such as acoustic metamaterials and phononic crystals, to manipulate
sound waves robustly, taking advantage of topological protection. Early work on
topological acoustics was limited to duplicating topological phases that have
been understood in condensed matter systems, but recent advances have shifted
the paradigm to exploring novel topological concepts that are difficult to
realize in other physical systems, such as various topological semimetal
phases, and topological phases associated with Floquet engineering, fragile
topology, non-Hermiticity and synthetic dimensions. These developments
demonstrate the unique advantages of topological acoustic systems and their
role in developing topological physics. In this Review, we survey the
fundamental mechanisms, basic designs and practical realizations of topological
phases in acoustic systems, and provide an overview of future directions and
potential applications.
