In this paper the ingredients of computing auditory perception are reviewed. On the basic level there is neurophysiology, which is abstracted to artificial neural nets (ANNs) and enhanced by statistics to machine learning. There are high-level cognitive models derived from psychoacoustics (especially Gestalt principles). The gap between neuroscience and psychoacoustics has to be filled by numerics, statistics and heuristics. Computerised auditory models have a broad and diverse range of applications: hearing aids and implants, compression in audio codices, automated music analysis, music composition, interactive music installations, and information retrieval from large databases of music samples.