Solidification of metals under a strong magnetic field is a new area for research.Here,some progress in the area is reviewed along with presentation of the fundamental effects of magnetic field.Focus is paid on the subjects of influence of a magnetic field on kinetics of solidification,instability of S/L interface,crystal growth of monophase alloy,eutectic growth,thermoelectrical magnetic convection and its effects,The core problems which should be investigated deeply and the key parameters needed are discussed.