Acoustic tweezers are gaining increasing attention as a noncontact method that is capable of handling microparticles and nanoparticles in a controllable manner. By designing the acoustic field, objects, such as cells, bacteria, exosomes, and even worms, could be precisely and flexibly manipulated by the acoustic radiation force. With the advantages of non-invasiveness, label-free operation, and low power consumption, acoustic tweezers have been proven to be crucially important for a diverse range of applications, particularly in the biomedical domain. In this paper, we review the historical development and the current state of the theory of the acoustic radiation force. Furthermore, we introduce recent advancements in acoustic tweezers based on the standing wave, travelling wave, single beam, and arbitrary wave fields; its mechanism and potential applications are also presented. Finally, some perspectives referring to the future development of acoustic tweezers are discussed.