The classical Neumann-Stefan problem (progress of crystallization from a quenched wall) can only be adapted to realistic situations if crystallization kinetics are introduced. After a review of the theoretical achievements attention is focused on the determination of the kinetic parameters which will enable us to simulate processes in isotactic polypropylene numerically, including the prediction of internal structures such as number (and size) of spherulites per unit volume and transcrystallization areas near the mold surface. Also with a proper measurement of the number of nuclei and of the growth speeds of spherulites as functions of temperature, heat transfer considerations play a key role. The influence of flow, which manifests itself in injection-molded parts by highly oriented surface layers, has separately been treated.