  Thermal convection in an electrically conducting fluid (for example, a liquid
metal) in the presence of a static magnetic field is considered in this
chapter. The focus is on the extreme states of the flow, in which both buoyancy
and Lorentz forces are very strong. It is argued that the instabilities
occurring in such flows are often of unique and counter-intuitive nature due to
the action of the magnetic field, which suppresses conventional turbulence and
gives preference to two-dimensional instability modes not appearing in more
conventional convection systems. Tools of numerical analysis suitable for such
flows are discussed.
