A comprehensive survey is presented of research on transport phenomena, that is, heat flow, fluid flow, mass transfer, and electrodynamics, associated with arc welding. Both gas-metal arc-welding (GMAW) and gas-tungsten arc welding (GTAW) systems are considered, and appropriate emphasis is placed on the intrinsic differences between these systems. The topics discussed include the behaviour of the arc, and its interaction with both the electrode and the surrounding medium, on the one hand, and the behaviour of the weld pool on the other. The limited work done on the coupling between arcs, electrodes, and weld pools is also discussed, as are some process-control issues, but the problems of thermal stress evolution and stress-induced deformation in the solid state are not treated. A critical discussion of the comparison between model predictions and experimental measurements is a key feature of the presentation, which concludes with a discussion of the critical problems that still need to be addressed.