We come to know about the world in two distinctive ways: by direct perception and by application of rational reasoning which, in its highest form, is mathematical thinking. The belief that the underlying order of the world can be expressed in mathematical form lies at the very heart of science. In other words, we only know what we can describe through mathematical models. Casting of metals has evolved first as witchcraft, to gradually become an art, then a technology, and only recently a science. Many of the processes used in metal casting are still empirical in nature, but many others are deep-rooted in mathematics. In whatever form, casting of metals is an activity fundamental to the very existence of our world, as we know it today. Foundry reports indicate that solidification modeling is not only a cost-effective investment but also a major technical asset. It helps foundries move into markets with more complcx and technically demanding work. The ability to predict internal soundness allows foundries to improve quality and deliveries, and provides the information required to make key manufacturing decisions based on accurate cost estimates before pattern construction even begins. The acceptance of computational modeling of solidification by the industry is a direct result of the gigantic strides made by solidification science in the last two decades.