The recent contributions on changes induced by high magnetic fields in transport phenomena, such as convection, solute diffusion, solute or phase migration in the liquid, are reviewed and analyzed. Selectivity provided by the Lorentz, thermoelectromagnetic (a special kind of Lorentz force), and magnetic forces or combinations enables the control of transport phenomena in liquids. This possibility, together with the capability of the transport phenomena to affect solidification in alloys, allows a level of control over solidification microstructures. As a result, recent relevant work can be found dealing with the effects of high magnetic fields on transport phenomena and the corresponding solidification microstructure evolution of alloys, based on the Lorentz, thermoelectromagnetic, and magnetic forces or combinations thereof.