Acoustic tweezers use sound radiation forces to manipulate matter without contact. They provide unique characteristics compared with the more established optical tweezers, such as higher trapping forces per unit input power and the ability to manipulate objects from the micrometer to the centimeter scale. They also enable the trapping of a wide range of sample materials in various media. A dramatic advancement in optical tweezers was the development of holographic optical tweezers (HOT) which enabled the independent manipulation of multiple particles leading to applications such as the assembly of 3D microstructures and the probing of soft matter. Now, 20 years after the development of HOT, we present the realization of holographic acoustic tweezers (HAT). We experimentally demonstrate a 40-kHz airborne HAT system implemented using two 256-emitter phased arrays and manipulate individually up to 25 millimetric particles simultaneously. We show that the maximum trapping forces are achieved once the emitting array satisfies Nyquist sampling and an emission phase discretization below pi/8 radians. When considered on the scale of a wavelength, HAT provides similar manipulation capabilities as HOT while retaining its unique characteristics. The examples shown here suggest the future use of HAT for novel forms of displays in which the objects are made of physical levitating voxels, assembly processes in the micrometer and millimetric scale, as well as positioning and orientation of multiple objects which could lead to biomedical applications.