In the quest to elucidate the solid-state structures of polymers, insight into the amorphous phase is particularly elusive. Although the permeability of small molecules is often measured as an important performance property, numerous researchers have found that a deeper analysis of the transport characteristics provides insight into polymer morphology, especially if used in combination with more usual characterization techniques. The transport of small gas molecules senses the permeable amorphous structure and probes the nature of the free volume. In recent years, our interest in the gas barrier of polyesters has resulted in an unusual opportunity to investigate the nature of the free volume in the polymer glassy state. This effort has been aided by access to aromatic polyesters with designed variations in their chemical structure. This review focuses on oxygen transport, supplemented with other methods of physical analysis, as a probe of the excess-hole free volume. The review addresses the profound effects of orientation and crystallization on the free volume of the glassy state. The discussion also presents a simple odel for the gas permeability of the isotropic glass based on lattice concepts and tests more sophisticated models for the gas permeability of semicrystalline polymers. The final section addresses other opportunities for fruitful applications of oxygen transport as a solid-state structure probe. (c) 2005 Wiley Pefiodicals, Inc.