We consider the three-dimensional ideal MHD system on a bounded domain, allowing boundary data to be prescribed on a designated controllable portion of the boundary. The basic question of boundary controllability is whether, given two states, one can drive the system from the first to the second through appropriate boundary controls. We review the existing results on this problem and establish exact boundary controllability for domains with Sobolev regularity. This is joint work with Wojciech Ożański.