There are many to contend that today human civilization has reached the age of engineered materials, yet the importance of iron castings continues to support the thesis that we are still in the Iron Age. Cast iron, the first man-made composite, is at least 2500 years old. It remains the most important casting material, with about 75 pct of the total world tonnage. This article is a review of the mathematical models that describe the fundamentals of solidification of iron-base materials, from the seminal articles by Jackson-Hunt (JH) and that of Oldfield, the first to attempt modeling of microstructure evolution during solidification, to the prediction of mechanical properties. The latest analytical models for irregular eutectics such as cast iron as well as numerical models with microstructure output (visualization models) are discussed. Because of space limitations, models for casting soundness are not included.