Metal vapour is formed in arc welding processes by the evaporation of molten metal in the weld pool, and in the case of gas-metal arc welding, in the wire electrode and droplets. The presence of metal vapour can have a major influence on the properties of the arc and the size and shape of the weld pool. Previous experimental and computational work on the production and transport of metal vapour in welding arcs, in particular those relevant to gas-metal arc welding and gas-tungsten arc welding, are reviewed. The influence of metal vapour on the thermodynamic, transport and radiative properties of plasmas is discussed. The effect of metal vapour on the distributions of temperature, current density and heat flux in arcs is examined in terms of these thermophysical properties. Different approaches to treating diffusion of metal vapour in plasmas, and the production of vapour from molten metal, are compared. The production of welding fume by the nucleation and subsequent condensation of metal vapour is considered. Recommendations are presented about subjects requiring further investigation, and the requirements for accurate computational modelling of welding arcs.