The magnetohydrodynamic model for fusion plasma dynamics governs the large-scale equilibrium properties, and sets the most stringent constraints on the parameter space accessible without violent disruptions. In conjunction with linear stability analysis in the complex tokamak geometry, the MHD paradigm is also routinely being used to diagnose recurring wave modes and identify potential MHD mode triggers of consequent non-MHD phenomena. On the other hand, it is currently computationally feasible to perform fully nonlinear simulations in tokamak geometry, and determine nonlinear, long-term (i.e. on resistive time scales) evolutions for individual MHD dominated plasma scenarios. It can be expected that this success continues its evolution towards a fully integrated computational analysis of the experimental campaigns, certainly in view of the desired steady-state self-burning plasmas.