The creation of thermal, compositional, and stress fields during the crystallization of polymers from the melt is described. The treatment of crystallization under self-generated fields is reviewed, including classical moving boundary problems, the treatment of dendrite growth, and coupled growth. The extension of these treatments to polymer crystallization requires that the velocity of interface motion be defined by the temperature and composition of the melt at the solid liquid interface, a feature not found in extant analyses suitable for small-molecule systems and metals. Inclusion of this feature renders analytical solutions difficult and usually requires the use of numerical methods. The role of the diffusion length in defining morphological features is described. Methods of simulating the growth of polymer spherulites are reviewed. These include finite element, analytical, and phase field approaches. The role of thermal fields in fiber processing is discussed. Finally, speculations regarding the role of stress fields are presented.