Arc plasma torches are the primary components of various industrial thermal plasma processes involving plasma spraying, metal cutting and welding, thermal plasma CVD, metal melting and remelting, waste treatment, and gas production. They are relatively simple devices whose operation implies intricate thermal, chemical, electrical, and fluid dynamics phenomena. Modeling may be used as a means to better understand the physical processes involved in their operation. This article presents an overview of the main aspects involved in the modeling of DC arc plasma torches: the mathematical models including thermodynamic and chemical nonequilibrium models, turbulent and radiative transport, thermodynamic and transport property calculation, boundary conditions, and arc reattachment models. It focuses on the conventional plasma torches used for plasma spraying that include a hot cathode and a nozzle anode.