Acoustic wave in solid has two modes of propagation: the bulk acoustic wave (BAW), which propagates inside solid in the form of longitudinal or transverse wave, and the surface acoustic wave (SAW), which is generated on the surface of solid and propagates along the surface. In acoustic radio frequency (RF) technologies acoustic waves are used to intercept and process RF signals, which are typified by the rapidly developing RF filter technology. Acoustic filter has the advantages of small size, low cost, steady performance and simple fabrication, and is widely used in mobile communication and other fields. Due to the mature fabrication process and well-defined resonance frequency of acoustic device, acoustic wave has become an extremely intriguing way to manipulate magnetism and spin current, with the goal of pursuing miniaturized, ultra-fast, and energy-efficient spintronic device applications. The integration of magnetic materials into acoustic RF device also provides a new way of thinking about the methods of acoustic device modulation and performance enhancement. This review first summarizes various physical mechanisms of magneto-acoustic coupling, and then based on these mechanisms, a variety of magnetic and spin phenomena such as acoustically controlled magnetization dynamics, magnetization switching, magnetic domain wall and magnetic skyrmions generation and motion, and spin current generation are systematically introduced. In addition, the research progress of magnetic control of acoustic wave, the inverse process of acoustic control of magnetism, is discussed, including the magnetic modulation of acoustic wave parameters and nonreciprocal propagation of acoustic waves, as well as new magneto-acoustic devices developed based on this, such as SAW-based magnetic field sensors, magneto-electric antennas, and tunable filters. Finally, the possible research objectives and applications of magneto-acoustic coupling in the future are prospected. In summary, the field of magneto-acoustic coupling is still in a stage of rapid development, and a series of groundbreaking breakthroughs has been made in the last decades, and the major advances are summarized in this field. The field of magneto-acoustic coupling is expected to make further significant breakthroughs, and we hope that this review will further promote the researches of physical phenomena of the coupling between magnetism and acoustic wave, spin and lattice, and potential device applications as well.