This thesis presents holograms as a novel approach to create arbitrary ultrasound ﬁelds. It is shown how any wavefront can simply be encoded in the thickness proﬁle of a phase plate. Contemporary 3D-printers enable fabrication of structured surfaces with feature sizes corresponding to wavelengths of ultrasound up to 7.5 MHz in water—covering the majority of medical and industrial applications. The whole workﬂow for designing and creating acoustic holograms has been developed and is presented in this thesis. To reconstruct the encoded ﬁelds a single transducer element is sufﬁcient. Arbitrary ﬁelds are demonstrated in transmission and reﬂection conﬁgurations in water and air and validated by extensive hydrophone scans. To complement these time-consuming measurements a new approach, based on thermography, is presented, which enables volumetric sound ﬁeld scans in just a few seconds. Several original experiments demonstrate the advantages of using acoustic holograms for particle manipulation. Most notably, directed parallel assembly of microparticles in the shape of a projected acoustic image has been shown and extended to a fabrication method by fusing the particles in a polymerization reaction. Further, seemingly dynamic propulsion from a static hologram is demonstrated by controlling the phase gradient along a projected track. The necessary complexity to create ultrasound ﬁelds with set amplitude and phase distributions is easily managed using acoustic holograms. The acoustic hologram is a simple and cost-effective tool for shaping ultrasound ﬁelds with high-ﬁdelity. It is expected to have an impact in many applications where ultrasound is employed.