i will report some recent works on structure-preserving and stable discretization of magnetohydrodynamics and robust preconditioning methods for the resulting algebraic systems. in particular, judging from theoretical and/or numerical analysis of several mathematical models for magnetohydrodynamics (mhd) which involve the coupling of navier-stokes with maxwell equations, i will argue that some more complicated models may be easier to simulate than some simplified models that have been often used in practice.