The paper gives an overview of the most common non-equilibrium approaches for modeling of tungsten-inert gas arc plasma, which have been developed up to date, in particular two-temperature and fully non-equilibrium approaches. The first group implies thermal non-equilibrium but chemical equilibrium whereas the second group describes the arc plasma avoiding assumptions of both thermal and chemical equilibrium. The common and specific features of the physical description are discussed. Results of the most recent fully non-equilibrium model, which is applied for the first time to tungsten-inert gas arc arrangement with a truncated conical tip of a doped tungsten cathode, are compared with those of previously published non-equilibrium models and experimental data. The general diffusion representation and more accurate boundary conditions incorporating the properties of the space-charge sheaths adjacent to the electrodes enable a novel description of the arc core, the near-electrode regions and the arc fringes in a self-consistent manner and provides a deeper insight into the arc properties.