Surface acoustic wave (SAW) is a new means of exciting and controlling spin wave (SW), which has not only high excitation efficiency, but also long transmission length up to millimeter order. Based on the SAW-SW coupling (phonon-magnon coupling), a wide variety of new devices and applications such as high-sensitivity weak magnetic field sensors, energy-efficient spintronic devices, solid-state acoustic isolators, and nonreciprocal phase shifters, have been realized. Therefore, it is of great value to study the physical mechanism of magneto-acoustic coupling, develop new magneto-acoustic coupling effects, and improve the efficiency of magneto-acoustic coupling. In this work, different types of physical mechanisms of magneto-acoustic coupling are reviewed. The effective driven magnetic fields of magnetoelastic coupling, spin-vorticity coupling (including injection of alternating spin current from a non-magnetic layer and Barnett effect inside magnetic material itself), and magneto-rotation coupling under different modes of SAW excitation are compared. The angular dependence of these driven fields and the frequency dependence of the corresponding power absorption are discussed, which provides theoretical support for distinguishing and utilizing various magneto-acoustic coupling in practical applications. In addition, we also introduce two methods to realize nonreciprocal SAW transmission by magneto-acoustic coupling, including the helicity mismatch effect and nonreciprocal spin-wave dispersion magnetic structures, and discuss their physical mechanisms as well as advantages and disadvantages. For such magneto-acoustic nonreciprocal devices, the properties of higher isolation, lower insertion loss and wider bandwidth are always desired. In order to improve the properties of the devices, it is important to find magnetic structures with stronger SW nonreciprocity, reduce the insertion loss introduced by magnetic structure, and fully consider the effective driven field characteristics of different modes of SAW. We hope that this review can serve as a guide for future design and development of solid acoustic isolators and circulators in the RF and microwave frequency bands.