Abstract: The concept of acoustic metamaterials was first proposed at the beginning of the 21st century, offering new ideas and methods for controlling acoustic fields in complex media. Therein, the multiple scattering of sound waves within the sonic/phononic crystals gives rise to a series of novel physical phenomena accompanied by unique dispersion relations. Recently, topological effects in condensed matter physics in classical wave systems have been drawing increased attentions. Acoustic metamaterials and sonic crystals provide an ideal experimental platform for studying topological effects, thanks to precise and controllable fabrication and measurement methods. A series of intriguing Hermitian and non-Hermitian topological effects have been realized in acoustic systems. The article reviews developments in the field of topological acoustics in recent years, starting from basic concepts and implementation schemes, and focuses on areas such as higher-order topological insulators, Hermitian/non-Hermitian topological systems, as well as functional topological acoustic devices and their applications in two-dimensional acoustic systems. Finally, an outlook on future development is provided.