Acoustic orbital angular momentum (OAM) associated with helicoidal wavefront recently attracts rapidly-growing attentions, offering a new degree of freedom for acoustic manipulation. Due to the unique dynamical behavior and inherent mode orthogonality of acoustic OAM, its harnessing is of fundamental interests for wave physics, with great potential in a plethora of applications. The recent advance in materials physics further boosts efforts into controlling OAM-carrying acoustic vortices, especially acoustic metasurfaces with planar profile and subwavelength thickness. Thanks to their unconventional acoustic properties beyond attainable in the nature, acoustic artificial structures provide a powerful platform for new research paradigm for efficient generation and diverse manipulation of OAM in ways not possible before, enabling novel applications in diverse scenarios ranging from underwater communication to object manipulation. In this article, we present a comprehensive view of this emerging field by delineating the fundamental physics of OAM-metasurface interaction and recent advances in the generation, manipulation and application of acoustic OAM based on artificial structures, followed by an outlook for promising future directions and potential practical applications.