The physics of the interaction between a liquid metals and an externally applied magnetic field is analysed starting from the basic equations of the phenomena involved: electromagnetic fields, fluid dynamics, viscosity and surface tension. A set of general equations is deduced to describe a levitation melting system. The equations are progressively simplified in order to highlight the most important contributions to the phenomena. The basis criteria for the design and operation of a cold crucible system are then described and together with some of the experimental results obtained.