A recent review pointed out that the existing models for gas tungsten arc coupling the electrode (a cathode) and the plasma are not yet complete enough. Their strength is to predict with good accuracy either the electric potential or the temperature field in the region delimited by the electrode and the workpiece. Their weakness is their poor ability to predict with good accuracy these two fields at once. However, both of these fields are important since they govern the heat flux to the workpiece through current density and temperature gradient. New developments have been made since then. They mainly concern the approaches addressing the electrode sheath (or space charge layer) that suffered from an underestimation of the arc temperature. These new developments are summarized and discussed, the modelling assumptions are examined, and important modelling issues that remain unexplored are underlined.