Welding defects such as undercuts, porosity, irregular beads are frequently observed in laser welds due to the fast cooling rate and no filler metal addition in the process. In addition, increasing penetration depth is a challenging issue in laser welding. Some preliminary experimental studies indicated that applying electromagnetic force in laser welding could be an effective solution to some of these problems. However, the underlying physics behind this electro-magnetically assisted laser welding is not clear and needs further investigation. In this paper, mathematical models are used to study the transport phenomena, such as heat transfer and melt flow, in both spot and 3-D electro-magnetically assisted laser welding. Studies are focused on understanding the effects of electromagnetic forces on heat generation and transfer, weld pool dynamics, cooling and solidification, porosity prevention, weld shape control, and penetration depth. Copyright © 2012 by ASME.