AbstractFirstly, we give a historical overview of attempts to incorporate magnetic fields into the Smoothed Particle Hydrodynamics method by solving the equations of Magnetohydrodynamics (MHD), leading an honest assessment of the current state-of-the-art in terms of the limitations to performing realistic calculations of the star formation process. Secondly, we discuss the results of a recent comparison we have performed on simulations of driven, supersonic turbulence with SPH and Eulerian techniques. Finally we present some new results on the relationship between the density variance and the Mach number in supersonic turbulent flows, finding σ²_{ln ρ} = ln(1 + b²² with b = 0.33 up to Mach 20, consistent with other numerical results at lower Mach number (Lemaster & Stone 2008) but inconsistent with observational constraints on σ_ρ and in Taurus and IC5146.