The contactless collective or selective manipulation of microscopic objects is powerfully enabled by acoustical tweezers. Trapping is achieved without pre-tagging with several order of magnitude larger forces at same input power than optical tweezers, limiting spurious heating and enabling damage-free displacement and orientation of biological samples. In addition, the availability of acoustical coherent sources from kHz to GHz frequencies enables the manipulation of a wide spectrum of particle sizes. After an introduction of the key physical concepts behind fluid and particles manipulation with acoustic radiation pressure and acoustic streaming, we will highlight the emergence of specific wave fields, called acoustical vortices, as a mean to manipulate particles selectively and in 3D. These acoustic vortices can also be used to generate hydrodynamic vortices whose topology is controlled by the topology of the wave. We will conclude this review by a viewpoint on the field future directions.