Consideration of crystallization kinetics in high molecular weight polymers shows that adjacent re-entry is unlikely in melt crystallization and that sections of individual chains will crystallize concurrently at several sites. Surface nucleation controlled growth models can be set up which do not require adjacent re-entry but are in agreement with observations on growth rates and crystal thicknesses. The predominant process in crystallization with random re-entry is the incorporation into the crystal of a loop of chain which has both ends attached to the crystal surface. This leads to predictions of the crystallinity of quenched, spherulitic polymers. Radii of gyration of chains in the crystalline state can be calculated and are in agreement with neutron scattering results.