One of the key technologies for developing materials science, microfabrication, and biomedical engineering is the manipulation of microparticles in microfluidic systems. Among the five main manipulation techniques, mechanical, electrical, magnetic, optical, and acoustic, acoustic manipulation has shown great promise because of its special benefits, which include label-free operation, biocompatibility, and efficiency in optically opaque surroundings. With an emphasis on surface acoustic waves (SAWs), bulk acoustic waves (BAWs), acoustic holography, and hybrid acoustic-optical platforms, this paper thoroughly investigates current advancements in acoustic manipulation techniques. In addition to outlining the governing equations and recent advancements in the field, this review paper addresses the key challenges, identifies research gaps, and explores future directions.