An overview is presented of transport phenomena in non-transferred plasma arc systems. It has been shown that while the modelling of these systems involves the standard application of computational fluid mechanics techniques, numerous pitfalls may be encountered in practice. A detailed discussion of these is presented, with emphasis on the torch inlet conditions, the effect of swirl, the temperature dependence of the system properties and the laminar-turbulent transition in the system. A critical comparison is presented with experimental measurements, and the necessary future work is also outlined.