Realizations of one-way manipulations in various kinds of energy flux are always highly desirable. The most famous example should be the invention of electric diodes which marked the emergence of modern electronics and resulted in worldwide technology revolutions. Acoustic wave, albeit a classical wave with much longer reflearch history in comparison with the electricity, has long been thought to propagate easily along two opposite directions in any path. Hence it should be intriguing to realize the one-way transmission of acoustic waves by designing the acoustical analogy of electric diodes, which would have deep implications in all the acoustics-based applications and the field of acoustics in general. In this review, we briefly describe reflent advances in acoustic one-way manipulation which has become a new frontier of science and is of remarkable significance in both the physics and engineering communities. The emergence of the first “acoustic diode”, formed by coupling a phononic crystal (PC) with a nonlinear medium, offers the possibility of rectifying acoustic energy flux by breaking through the barrier of reciprocity principle via the introduction of nonlinearity. Despite of the efforts in enhancing the performances of nonlinear acoustic diodes by updating their structures, the inherent shortcomings in nonlinear systems such as low efficiency and narrow bandwidth still attract considerable attentions on the potential of linear structures, aiming at constructing a one-way manipulation on particular modes of an acoustic wave without breaking the reciprocity principle. A series of linear acoustic one-way devices have already been designed and fabricated with significantly improved performances. On the basis of asymmetric mode conversion, a linear one-way plate for Lamb waves is designed. High efficient one-way transmission for plane waves propagating along two opposite directions is realized by coupling a PC and a diffraction structure. Unidirectional waveguide is designed and fabricated which only allows for a plane wave incident from one of the two openings to pass. A unidirectional structure with a total thickness as thin as the wavelength is realized by reconstructing the otherwise plane wavefront with acoustic gratings. An acoustic gradient-index structure is proposed that can directly manipulate the wave trajectory asymmetrically and then yield asymmetric acoustic transmission within a considerably broad band. Acoustic metamaterials with near-zero indexes have also been employed to realize unidirectional transmission with a controllable transmitting angle and consistent wavefront. These advances are important steps towards the practical applications which generally require integration and minimization of devices having high efficiency and broad bandwidth. The reflently emerged “acoustic transistor” has been described as well, which can be regarded as the acoustical counterpart of an electric transistor and enables the amplification and switch of acoustic waves by an acoustic wave, or by exploiting the three-wave mixing effect. We also discuss the challenge and promise of the usage of acoustic one-way devices in controlling acoustic waves.