Latest developments in thermoacoustic devices have demonstrated comparable power output and efficiency, but higher reliability and lower cost when compared to conventional low-grade heat recovery technologies. A good coupling between multiple physical fields plays a pivotal role in realizing these potentials. This article provides a comprehensive review of the multi-physics coupling effects, namely, thermal-acoustic coupling, acoustic-mechanical coupling and mechanical-electric coupling, inside thermoacoustic devices including thermoacoustic engines, thermoacoustic electric generators, thermoacoustically-driven refrigerators, etc. The basic principles, operating characteristics, design strategies and future prospects are discussed individually for each coupling effect. System-level design techniques and synthetic optimization methodologies in consideration of the multi-physics coupling effects are presented. This review work gives insights into the underlying mechanisms of various coupling effects in thermoacoustic devices and provides guidelines for improvements of modern thermoacoustic technologies for low-grade thermal energy recovery, refrigeration and electric power generation purposes.