It is surprising that polymers such as polyolefins, composed only of carbon and hydrogen atoms in very simple configurations, can be used in so diverse applications as human bone prosthetic implants, gas pipelines, car bumpers, synthetic fibers, and plastic films. The reason for such versatility is that microstructural. characteristics of polyolefins, such as distributions of molecular weight, chemical composition (or short-chain branching), and long-chain branching, have an enormous impact on their macroscopic properties and applications. Therefore, it is of utmost importance that these microstructural. details be well understood and properly described with fundamental models. This manuscript reviews the state-of-the-art mathematical modelling techniques for describing the microstructure of polyolefins produced by coordination polymerization.