Laser material processing, that means cutting, welding and surface treatment with highly focused high power laser beams experiences rising interest all over the world, because these machining processes show important advantages compared to conventional processes, as for instance, largely increased processing speed, high processing quality, low noise production and no environmental pollution. From all these laser machining processes laser cutting has reached the highest degree of maturity and several companies offer laser cutting facilities on the market from series production. By the way, it was an Italian company that introduced the first time successfully a three-dimensional laser cutting system. Nevertheless, there is a strong demand for further improvements either in terms of cutting speed, cutting quality or maximum thickness that can be separated. In order to obtain these improvements the physical mechanism of the laser cutting process has to be fully understood and theoretical models must be available to be able to predict the influence of improved beam properties,as for instance, enhanced laser power on cutting performance and quality. Due to the importance of physics and theory of laser cutting in that paper an overview over these topics is provided.