We consider the three-dimensional ideal MHD system on a domain in  with a controllable part of the boundary where we prescribe the boundary data. The basic question of boundary controllability is whether, given two states, one can by means of the control on the boundary drive one state to another. We will review the existing literature on this problem and provide a positive result for domains with only Sobolev regularity. The results are based on works with Matthew Novack, Wojciech Ozanski, and Vlad Vicol.