Supercooling before crystallization is well known for over 300 years and has been linked to the need of crystal nucleation. The nucleation is then followed by crystal growth, which usually quickens with increasing supercooling, goes through a maximum, and finally decreases again as the molecular mobility decreases when approaching the glass transition temperature. Superheating, in contrast, is less common. Very often melting is sufficiently fast so that its rate is determined by the conduction of the heat of fusion into the crystal, i.e., on heating, the temperature does not rise above the melting temperature until the end of the transition. Some 100 years ago, superheating was first studied. It was observed that nucleation of the mobile phase usually does not slow down the melting. Only slow melting leads to superheating. The molecular mobility increases with temperature and reduces at higher temperatures the chance of superheating. Both, supercooling and superheating are discussed on hand of theories developed for simple motifs. The results are then expanded to semicrystalline polymers which represent an arrested, metastable system with locally reversible subsystems. The macromolecules may bridge between crystal and fluid phases at points of decoupling and transfer stresses across the phase boundary. This can develop more viscous environments around the crystals. A more viscous environment, in turn, slows phase transitions, as does the need of specific conformations for the transition. Order in the amorphous phase, in contrast, increases the equilibrium phase transition, not necessarily the superheating. Crown Copyright (C) 2006 Published by Elsevier B.V. All rights reserved.