A theory has been developed which predicts the minimum permeability that can be expected for a polymer filled with platelike particles. Models are also developed for the permeability of liquids through filled polymers when the liquid adsorbs or collects at the filler-polymer interface. Some of the cases discussed include different types of dispersions, orientation of filler particles, and the effects of filler aggregation. Permeability, especially of liquids, is extremely complex, and many different types of behavior can be expected.