The metallurgical and mechanical properties of fusion welded joints are influenced, among others phenomena, by the weld pool dimension and shape. Weld pool shape is important in the development of grain structure and dendrite growth selection process as well as in the development of residual stresses. For these reasons, significant advances have been made in recent years to understand, in greater detail, the dynamics of the heat and fluid flow in the weld and the subsequent development of the pool shape. In numerical simulation of welding processes, there are two different approaches used to model the fusion zone. If the prediction of distortions and residual stresses is the primary objective of the simulation (computational weld mechanics simulation), the phenomenological approach is the most suitable method used to model the fusion zone. Otherwise, when the weld pool shape has to be predicted, the fluid-dynamic equations must be solved at the expense of a significant ‘computational load’ increase. In this work, after a brief description of weld pool characteristics, such two different approaches are described and compared.