A brief history of the progress in the field of polymer crystallization has been reviewed from the viewpoints of the author`s 30 years research. Why the polymer chains are folded on crystallization is the main topic. First, whether the equilibrium theory or the kinetic theory is aright for explaining the chain folding was discussed. Next, the effect of molecular weight on the chain folding was discussed, involving the lamellar thinning and thickening into the once-folded chain crystals and the extended chain crystals for low molecular weight poly(ethylene oxide) fractions and pure long n-alkanes. Thirdly, the effect of the chain flexibility on the chain folding was discussed on the crystallization of poly(chloro-trifluoroethylene) and poly(tetrafluoroethylene), which are comparatively inflexible. Crystallization of cellulose from its dilute aqueous solutions of sodium hydro-oxide was also discussed, which gave the chain folded crystals and the extended chain crystals, depending on the solvent. Next, crystallization during polymerization was discussed for many instances, where the extended chain crystals and other unique morphologies were formed. Further, the researches on the fold structure of polymer crystals were briefly reviewed in view of our studies on crystallization of random and block copolymers. Crystallization of random copolymers of ethylene and vinyl acetate indicated the possibility of the formation of fringed micell structure. Finally, crystallization under molecular orientation was reviewed mainly from our experimental results. From these results, we concluded that the origin of the folds lies in the polymer conformations in the molten or solution state.