Acoustic waves in solids have two modes of propagation: the bulk acoustic wave (BAW), which propagates inside solids in the form of longitudinal or transverse wave, and the surface acoustic wave (SAW), which is generated on the surface of solids and propagates along the surface. Acoustic radio frequency (RF) technologies utilize acoustic waves to intercept and process RF signals, which are typified by the rapidly developing RF filter technology. Acoustic filters have the advantages of small size, low cost, steady performance and simple fabrication, and are widely applied in mobile communications and other fields. Due to the mature fabrication process and well-defined resonance frequency of acoustic devices, 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 devices has also provided a new way of thinking about the means of acoustic device modulation and performance enhancement. This review firstly 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 progress of research on 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, tunable filters, and so on. Finally, possible future research goals and applications of magneto-acoustic coupling are envisioned. In summary, the field of magneto-acoustic coupling is still in a stage of rapid development, and a series of groundbreaking breakthroughs have been made in the last decades, and this paper summarizes the major advances in this field. The field of magneto-acoustic coupling is expected to make further significant breakthroughs, and we hope that this review will further advance the physical phenomena of the coupling between magnetism and acoustic wave, spin and lattice, as well as the potential device applications.