Hardware devices that can implement computed holograms, which encode user-defined (mostly) amplitude distributions, have enabled various novel applications in acoustics. Phased arrays of transducers (PATs) have led multisensory point-based displays (PBDs), while diffraction limited acoustic fields by subwavelength passive holograms have found application in matter manipulation and fabrication, where field accuracy is more crucial. The main distinction between these applications is the hardware’s ability to rapidly switch between different holograms, which requires different approaches in sensing and modelling the acoustic field, and, consequently, different phase retrieval (PR) algorithms for computing holograms. In this lecture, we first review point, image and mesh based methods and their corresponding acoustic propagation models. We then demonstrate that Gerchberg-Saxton based PR performs better in applications like PBDs by PATs, when the field is sampled a small set of focal points. On the other hand, optimizing over L2-norm amplitude objectives is preferable when the target field is more densely sampled and thus complicated. Finally, we manipulate the regularization term in PR to give solutions to practical hardware challenges in dynamic holography. We believe that robust modelling and computing of acoustic holograms is essential for fulfilling their full potential and designing novel dynamic passive holographic metamaterials.