Feature Article: From the viewpoint of controlled polymer synthesis, topochemical polymerization based on crystal engineering is very useful for controlling not only the primary chain structures but also the higher-order structures of the crystalline polymers. We found a new type of topochemical polymerization of muconic and sorbic acid derivatives to give stereoregular and high-molecular weight polymers under photo-, X-ray, and gamma -ray irradiation of the monomer crystals. In this article, we describe detailed features and the mechanism of the topochemical polymerization of diethyl-(Z,Z)-muconate as well as of various alkylammonium derivatives of muconic and sorbic acids, which are 1,3-diene mono- and dicarboxylic acid derivatives, to control the stereochemical structures of the polymers. The polymerization reactivity of these monomers in the crystalline state and the stereochemical structure of the polymers produced are discussed based on the concept of crystal engineering, which is a useful method to design and control the reactivity, structure, and properties of organic solids. The reactivity of the topochemical polymerization is determined by the monomer crystal structure, i.e. the monomer molecular arrangement in the crystals, Polymer crystals derived from topochemical polymerization have a high potential as new organic crystalline materials for various applications. Organic intercalation using the polymer crystals prepared from alkylammonium muconates and sorbates is also described.