Fusion welding (gas metal arc welding, laser welding, etc.) is a major joining technique adopted by many industries like auto, aerospace, shipbuilding, etc. Depends on applications, some require deep welding with strong bonding, some require small heat affected zones in welds (HAZ), some may require fast welding speed with good weld quality. In order to meet these requirements and achieve quality welds with no porosity and cracking, heat transfer and fluid flow processes must be well understood. However, there are many factors (process parameters) in real welding that can affect the heat transfer and fluid flow in weld pool and subsequent welds, thus affecting the quality of the final weld, studies of welding processes through traditional trial-and-error approach is very time consuming and becomes very challenging especially when studies of dynamics phenomena in welding are required. With the recent improved understandings of the welding physics and advance of computational techniques, computer modeling of welding processes is getting feasible. In this study, a comprehensive mathematical model and the associated computational modes will be developed and used to study transient energy transfer and melt flow in laser-based welding, thus providing an effective tool to further study and optimize laser-based welding processes to achieve quality welds.