Thermal plasmas generated by electric arc discharges between various types of electrodes or by plasmatrons have many well-established-and numerous potential-applications in extractive metallurgy, materials processing and high temperature chemistry. The current is from below 100 A in welding arcs to above 100 kA in electric arc furnaces (EAF) for steel-making and submerged arc furnaces (SAF) for production of silicon alloys. AC as well as DC is used. To improve process understanding and equipment design a number of simulation models have been developed, reaching higher levels of sophistication as more computer capacity has become available. This report reviews the state-of-the-art of arc simulation and discusses some important problems and challenges for future modelling work-in particular on high currents and AC operation. The perspective is the metallurgical and chemical engineers' demand for practical simulation models-not the physicist's very stringent approach.