Inspired to discoveries in condensed matter systems, topological insulators (TIs) for classical waveWaves systems have been recently unveiled in various platforms. AcousticsAcoustics in particular offers a well-established playground to realize topological phases and probe their unique features. AcousticAcoustics TIs open a wealth of exciting applications, such as robust routing of soundSound, resilient signal pro-cessing, switching, etc. This Chapter provides an overview of recent progress in the discovery of topological phenomena in acousticsAcoustics and the associated underlying realizations, ranging from simple one-dimensional analogues of the Su–Schrieffer–Heeger model to Chern insulators, spin-Hall insulators, valley-Hall insulators, Weyl semimetals, and higher order TIs.