ABSTRACT
The basic nature of MHD waves is well understood. In the geospace and solar environments, as well as in other astrophysical situations, there are many unsolved problems that arise from the structure of the environment. They will be solved by modelling the region in which the MHD waves occur and its boundaries, rather than by new understanding of the theory of the waves. One is that of the basis of the MHD approximation and the nature of the collision-like interactions that make an ostensibly collisionless medium frequently behave as an MHD fluid with isotropic pressure. One might equally consider the unreasonable effectiveness of single-fluid MHD in describing phenomena in astrophysics and space science. Most of the other problems are those of extension of the theory to include nonlinear effects. Much progress has recently been made in understanding nonlinear processes but much remains to be done.
