The process of solidification is the same in all cases, whether it is the freezing of water on a windshield or in a freezer or the solidification of metal in a casting or in the weld that joins two solids. This article discusses the solidification of alloy welds and provides a comparison of casting and welding solidification. The constitutional supercooling model for describing weld solidification is presented because it qualitatively describes the evolution of different weld microstructures. The article describes the welding rate effect on weld pool shape and microstructure, as well as the nonequilibrium effects.