Outstanding Theoretical Problems

The development of model atmospheres from the 'classical' static but deductive models to present-day dynamic but inductive models is sketched. The main problems facing theory are defined in terms of the need to produce a post-classical inductive model. Attention is focused on the most promising tool available today, the computers able to realize simulations of astrophysical systems. The direction of progress in the areas of radiative transfer, convective transport, waves and oscillations, and MHD is reviewed. It is concluded that the major outstanding radiative and hydrodynamic problems are likely to be elucidated in the foreseeable future, especially if there is a suitable commitment by the international community. However, the understanding of the behaviour of magnetic fields and their associated activity will require a longer, but no less urgent, programme.