Ground-based and satellite observations have shown that all late-type dwarfs possess hot outer envelopes, and that the chromospheric and coronal emissions observed from these envelopes vary significantly for a given, fixed spectral type. In addition, there is growing evidence for nonhomogeneous and locally strong magnetic fields in the atmospheres of these stars. It is obvious that any heating theory must account for these two observational constraints as well as for the mean level of heating.
There are at least two general classes of models that deal with the required heating. The first class assumes that outer stellar atmospheres are heated by hydrodynamic (mainly acoustic) or magnctohydrodynamic (MHD) waves, and that these waves are generated by turbulent motions in the stellar convection zones. The second class considers dissipation of currents generated by photospheric motions as the primary source of energy. Neither observation nor theory has been able to definitively determine which one of these two general classes of models dominates in the atmospheric heating. The main aim of this paper is to briefly present recent developments in the MHD wave heating theory. The key problems that will be addressed are: where and how efficiently are MHD waves generated, and how do these waves propagate and dissipate energy?