In its first part, this review paper discusses skin morphology and barrier function of the stratum corneum for drug permeation after its transdermal administration or topical application. Further, the paper presents the main methods for overcoming the skin permeation barrier, which plays an important role for transdermal drug administration. Focus is on the method of chemical permeation enhancement. The chemical enhancers are categorised by their chemical structure. Examples of the most effective enhancers are given for the chemical groups of alcohols, amines and amides, polyalcohols, terpenes, fatty acids and their esters, macro cyclic compounds, sulfoxides, tensides, and others, as e.g. soft enhancers.