Skin Structure and Physiology -- Methods for the Measurement of Percutaneous Absorption -- Mathematical Treatments and Early Models of Skin Permeability -- "Building error upon error": The New Breadth of Research in the Field -- Algorithms for Estimating Permeability Across Artificial Membranes -- Other Approaches to Modelling Percutaneous Absorption -- "Squiggly lines and random dots - you can fit anything with a non-linear model" -- Finite-dose models of transient exposures and volatile formulation components -- "The Devil Is in the Detail ..." -- Conclusions and Recommendations for Model Development and Use.