Permeability is broadly defined as the ability of a material to allow the transportation of liquids, gases, or vapors through it. Although numerous references can be found in the literature giving the permeability values of polymers, there is no standard unit of gas or vapor transport, making comparisons difficult. This review summarizes the permeability of single polymer films used in book and paper conservation, specifically addressing the permeability of storage materials and processes such as encapsulation. In particular, the permeability of the polymer films to oxygen, nitrogen, hydrogen sulfide, water vapor, and acetic acid is summarized. The permeability was found to differ by over 7 orders of magnitude when comparing different gases and vapors diffusing through the polymer films. The permeability is dependent on the molecular size of the diffusing gas or vapor, with smaller molecules diffusing faster than larger molecules. In addition, the chemistry of the film plays a role. Hydrophilic polymers have a much greater permeability of polar diffusants such as water vapor than hydrophobic polymers. In addition, the permeation increases significantly with temperature. The review provides data of the permeability properties of the films used by conservators and will enable them to make an informed decision of the best material for their application.