  This contribution contains the introductory remarks that I presented at IAU
Symposium 270 on ``Computational Star Formation" held in Barcelona, Spain, May
31 -- June 4, 2010. I discuss the historical development of numerical MHD
methods in astrophysics from a personal perspective. The recent advent of
robust, higher order-accurate MHD algorithms and adaptive mesh refinement
numerical simulations promises to greatly improve our understanding of the role
of magnetic fields in star formation.
