Acoustic waves are classical mechanical waves that propagate in an elastic medium. When they reflect, refract and scatter on the surface of objects, momentum and energy exchange will be generated, which is manifested as a force exerted on the object macroscopically, called the acoustic radiation force. Two scientists, Rayleigh and Langevin, first discovered the phenomenon of acoustic radiation force. Through the exploration of more than one hundred years, the fundamental theories and investigations of acoustic radiation forces have been greatly enriched and developed, becoming the frontier issues of acoustics. Meanwhile, in the fields of biomedicine, material science and nanoscience, the non-destructive precise manipulation technology based on acoustic radiation force is receiving increasing attention, showing great prospects in real applications.