Mean field magnetohydrodynamics is a theoretical framework that uses averaged versions of the induction equation and the equation of motion to model large-scale gas flows and the generation of large-scale magnetic fields in astrophysical bodies. This method is computationally cheap and has been used with some success in astrophysics but requires a theory of the effect of the small scale gas motions on the large scale motions and magnetic field. More recently, advances in high performance computing have made direct numerical simulations feasible. We show results from both approaches.