The classical electrochemistry of the electrical double layer appropriate to materials that operate as electrodes is shown to be a limiting description for non-electrode materials such as clays, inorganic oxides, insoluble salts, latex colloids and biosurfaces. The following unified treatment is valid in the first instance for double layers where the surface charge results from ionization of discrete identifiable surface sites. The major surface and bulk parameters that control such models are illustrated and principal trends and effects, in particular the non-Nernstian behaviour of such surfaces, are illustrated.