The latest research on dynamics of grain boundaries in non-magnetic materials in high magnetic fields is reviewed. A control of grain boundary migration means control of microstructure evolution, which is a key for the design of materials with desire properties. Grain boundary motion can be affected by a magnetic field, if the anisotropy of the magnetic susceptibility generates a gradient of the magnetic free energy. In contrast to curvature driven boundary motion, a magnetic driving force also acts on planar boundaries so that the motion of crystallographically well-defined boundaries can be investigated, and the true grain boundary mobility can be determined. The results of migration measurements obtained on bismuth and zinc bicrystals are addressed. Selective growth of new grains in locally deformed zinc single crystals driven by a magnetic force is reported as well. Implications for materials processing, in particular the effect of magnetic fields on texture development in hcp metals are finally discussed.