Polymer molecules are characterized by the unique structural feature of being composed of a large number of chain units covalently linked together. Despite this complexity of structure macromolecular systems still retain the ability to exist in different states, a property common to all substances. Two of the states of matter observed for monomeric substances, the liquid and crystalline states, are also found in polymeric substances. The liquid or amorphous state is characterized by the fact that, because of the freedom of rotation about the bonds connecting the chain atoms, a single polymer molecule can assume a large number of configurations. In this state, therefore, the chain units of different molecules are arranged in a random, disoriented array uncoordinated with one another. Under appropriate thermodynamic conditions, however, a spontaneous ordering of portions of the chain molecules can occur, and in contrast there results a state of configurational order, the freedom of rotation being lost. This latter state is termed the crystalline state. Major attention in this review is directed to the consideration of the transformation from the crystalline state to the liquid state. Certain closely related subjects as the morphology and organization of the crystalline state and the mechanisms and kinetics of crystallization from the melt have been recently reviewed and hence will not be considered in any great detail. The melting process that occurs in various types of polymeric systems will be considered and conclusions drawn from the presently available evidence. Presentation from a unified point of view, based on certain fundamental considerations, is aimed for. The basic underlying principles which govern the phenomena will be stressed; experimental results which demonstrate these principles or point out the need for new developments will be presented. An effort will be made to consider problems from the point of view of theoretical expectations and experimental findings. On the other hand, no effort is made to include a description of all work in this field, although care has been taken to be as comprehensive as possible in discussing the basic principles.