The assembly of long-chain polymers into an ordered state is a process that has puzzled polymer scientists for several decades. A process that is largely controlled by the strength of intermolecular attractions in small molecular systems, this crystallization in the case of polymers is controlled by a competition between the aforementioned force of attraction between monomers and the formidable conformational entropy of polymer chains. Any factor that affects this conformational entropy, whether that is an equilibrium thermodynamic factor or a kinetic factor, has the ability to control polymer crystallization. In this thesis, we focus on understanding the underlying kinetic processes that occur during this phase transition from liquid polymer to the solid semicrystalline state using computer simulations and some experiments. We first investigate the effect of chain ends on crystallization by comparing between the crystallization behavior of linear and ring polymers of the same molecular weight using Langevin dynamics simulations. We find single linear polymers to melt at much larger temperatures than single ring polymers, in apparent contradiction of equilibrium thermodynamic arguments. We study several kinetic factors, and find that they explain this discrepancy. We then study the melting of linear polymers by Langevin dynamics simulations to understand the processes occurring during their disassembly. We find that polymer chains go through a globular metastable state at lower melting temperatures before transforming to expanded coils at higher melting temperatures. We also compute a free energy landscape using parallel tempering Langevin dynamics simulations, and confirm the existence of metastable states in the crystalline-amorphous reaction coordinate. We look at the crystallization of triblock copolymers using Langevin dynamics simulations, in which crystallizable blocks are separated by non-crystallizable ones to understand the effect of impurities. We investigate the effects of tailored interblock and solvent-block interactions, and discover a rich system in which the final semicrystalline polymer forms an array of morphologies. We also experimentally investigate the crystallization of calcium oxalate, which is a primary constituent of kidney stones. We crystallize calcium oxalate and show images of crystals obtained from an optical microscope. Lastly, we extend the scope of our studies into the effect of impurities by looking at crystallization of branched polymers. We discover that branches affect the kinetics of crystallization when they are in close proximity with one another.