The problem of pressure fluctuations at a rigid wall under a turbulent boundary layer has attracted much attention in the past decade. At low Mach numbers the theory is well established from the work of Kraichnan and Lilley, and reasonable agreement is obtained with the experiments of Willmarth, Hodgson and others. At high Mach numbers, measurements exist due to the work of Kistler and Chen but so far no theory is available, apart from that due to Phillips, which is however related to the noise radiated from supersonic turbulent shear flows. The present paper reviews the theory of wall pressure fluctuations in incompressible flow, and shows how the character of the pressure fluctuations changes in passing from the flow to the wall. Attention is drawn to the more important interactions giving rise to the pressure fluctuations, as well as to the region of the boundary layer mainly responsible for the wall pressure fluctuations … [cont.].