The review is written from the point of view of an engineer wanting to understand, reduce, and predict noise from turbomachines. In consequence knowledge gained by theory and, in particular, experiment is emphasized rather than the details of theoretical treatments. Attention is drawn to the surprisingly small interaction between theory and experiment and to the small amount of application that the theories have received. In describing the theoretical models it is the validity or applicability of their assumptions that is emphasized; despite the large number of theoretical treatments published the range of assumptions is quite small. Inevitably the review reflects the emphasis on funding for research by describing mainly high-speed, aeronautical turbomachinery noise. The overall conclusions drawn are rather depressing, with relatively little known even now about noise mechanisms for high speed machinery.