Historical perspective on astrophysical MHD simulations

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.