Transdermal drug delivery is a rapidly expanding industry with significant advantages over conventional oral and intravenous methods. However, in order to gain a better understanding of drug permeation mechanisms and obtain accurate estimates of drug permeability to the skin, there is an urgent need for modeling techniques. In this thesis, we present a multi-scale modeling approach to investigate solute transport through the human stratum corneum. Firstly, continuum finite element brick-and-mortar models were constructed to study water permeation. Subsequently, molecular dynamics simulations were employed to investigate the permeation of various solutes through lipid bilayers within the stratum corneum. [...]