Solid-state transformations from invariant reactions are of three types: eutectoid, peritectoid, and monotectoid transformations. This article focuses on structures from eutectoid transformations with an emphasis on the classic iron-carbon system of steel. It illustrates the morphology of a pearlite nodule and the effect of various substitutional alloy elements on the eutectoid transformation temperature and effective carbon content, respectively. Peritectic and peritectoid phase equilibria are very common in several binary systems. The article reviews structures from peritectoid reactions and details the formation of peritectic structures that can occur by at least three mechanisms: peritectic reaction, peritectic transformation, and direct precipitation...