A major goal in solar physics has during the last five decades been to find how energy flux generated in the solar convection zone is transported and dissipated in the outer solar layers. Progress in this field has been slow and painstaking. However, advances in computer hardware and numerical methods, vastly increased observational capababilities and growing physical insight seem finally to be leading towards understanding. Here we present exploratory numerical MHD models that span the entire solar atmosphere from the upper convection zone to the lower corona. These models include non-grey, non-lte radiative transport in the photosphere and chromosphere, optically thin radiative losses as well as magnetic field-aligned heat conduction in the transition region and corona.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html