Fluid flow and solidification during welding dominate the fusion zone of the resultant weld, including its shape, microstructure, properties, and defects. Fundamental research conducted at the University of Wisconsin led to the first demonstrations of the following things in four different areas. The first area, fluid flow in welding, includes: 1) computer models capable of calculating the weld-pool shape and showing how weld-pool fluid flow affects the pool shape, including Marangoni flow driven by surface-tension gradients along the pool surface, 2) visualization of Marangoni flow in simulated weld pools, including its reversal by the surface-active agent and its oscillation, and 3) a theory on the effect of the surface-active agent on pool-surface deformation, pool-surface oscillation and ripple formation as well as weld penetration. The second area, solidification in the fusion zone, includes 1) quenching of the weld pool and its surroundings to reveal the microstructure development, microsegregation, and nucleation mechanisms during welding, e.g., with liquid Sn for stainless steels and water for Al alloys, and 2) suppression of solidification cracking with a wavy crack path, as demonstrated by transverse magnetic arc oscillation in welding of Al sheets. The third area, solidification in the partially melted zone (PMZ), includes: 1) weakening of the PMZ by severe grain-boundary segregation caused by planar solidification of the grainboundary liquid, as demonstrated in arc welds of high-strength Al alloys, and 2) prediction and elimination of the susceptibility of Al alloys to liquation cracking, i.e., cracking in the PMZ along grain boundaries where liquid formation (i.e., liquation) occurs. The fourth area, solidification with dissimilar filler metals, includes 1) fundamental concepts in welding with dissimilar filler metals, including non isothermal pool boundaries and quick freezing of one liquid metal in another to cause macrosegregation, and 2) macrosegregation mechanisms based on the concepts to explain the formation of beaches, peninsulas, and islands different in composition from the bulk weld metal (i.e., bulk fusion zone).