Synthetic polymers are produced via a multitude of reaction mechanisms and processes, including addition (e.g. free-radical, ionic, group-transfer, Ziegler-Natta coordination) and step-growth polymerizations. A major objective of polymerization reaction engineering is to understand how the reaction mechanism the physical transport processes (e.g. mass and heat transfer, mixing), reactor configuration and reactor operating conditions affect the macromolecular architecture (e.g. molar mass, molecular weight distribution, copolymer composition distribution, branching distribution stereoregularity, etc.) as well as the morphological properties of the polymer product (e.g. particle size distribution, porosity, etc.). As the polymer industry becomes more competitive, polymer manufacturers face increasing pressures for production cost reductions and more stringent "polymer quality" requirements. To achieve these goals one needs to develop comprehensive mathematical models capable of predicting the molecular and morphological properties in terms of reactor configuration and operating conditions. These mathematical representations can be classified into microscale kinetic models mesoscale physical, transport and thermodynamic models and dynamic reactor ones. The present paper provides an overview of the different polymerization processes and mathematical modeling approaches. It is also addresses the problems related with the computer-aided design, monitoring optimization and control of polymerization reactors.