This is the text of an introductory lecture intended to provoke discussion of some of the problems likely to face participants in the Workshop as they develop the subject of Computational Aeroacoustics (CAA). Many of the points were already made by the author in a lecture at the 1st IMACS Symposium on Computational Acoustics (Crighton, 1988). Nonetheless, it is appropriate to repeat and amplify them in a Workshop devoted specifically to CAA and not to the wider problems of acoustics — and in particular, in a Workshop in which it is hoped that interest and expertise will have been brought together in more than the critical mass needed to really make CAA take off as a significant tool in aeroacoustics investigations.