This article reviews the development and application of Computational AeroAcoustics (CAA) to acoustic propagation on subsonic mean flows, with a particular focus on methods used to predict acoustic radiation from turbofan aeroengines. The governing equations are presented and particular issues such as the formulation of impedance and far field boundary conditions, the treament of Kelvin-Helmholtz instabilities, resolution requirements and methods for controlling dispersion error, are discussed. The status of current CAA methods is reviewed. Finally, the matter of validation against benchmark problems and measured data is explored.