This paper includes a theoretical description of some of the major physical phenomena of thermal cutting processes in general. The work is mainly focussed on the laser cutting process. Qualitatively and some quantitatively descriptions of the melt front propagation and the melt flow is described. The theory, supported by experimental studies shows, that in high quality thermal cutting, the melt flow is in front of the cut kerf with a uniform pressure at the melt surface. Furthermore is shown, that at high cutting rates, evaporation in the lower central part of the cut kerf forces the melt partially around the laser beam, reducing the cut quality. Theoretical estimation of the melt film thickness in thermal cutting is derived. It is shown that there is a maximum cutting speed, where substantial evaporation in the cut front can be neglected. This maximum cutting speed depends upon the thermal properties of the material, the thickness of the material and the pressure from the cutting gas. Furthermore the paper indicates thermal instabilities in the top of the cut front in thermal cutting processes, which is supposed to be responsible for the striation formation.