The thermal bulk polymerization of styrene is critically reviewed. There is still no generally accepted kinetic model for the thermal radical formation process, but ideal second- or third-order models are widely used for modeling bulk systems. Since initiation and chain transfer reactions cannot be treated independently from one another as long as the same species is considered to be involved, it is concluded that non-ideal kinetics, possibly in form of a (micro-)viscosity dependency of the Mayo mechanism, are likely to be present. A mathematical model is presented that keeps the predictive capabilities of the Hui-Hamielec model, but allows facile implementation of reaction specific modifications. Part 2 of this paper will focus on the effect of compartmentalization on the thermal polymerization of styrene.