Controlled drug delivery systems are vital for successfully treating a wide range of diseases. Mathematical models are essential in developing new polymeric and transdermal delivery systems. In this dissertation, mathematical models have been built to investigate the effects of multiple transport mechanisms on drug delivery. A compartmental model of drug release from polymeric devices is used to simulate diffusion and surface erosion simultaneously. The effects of particle polydispersity, instantaneous binding and hydrophilic shells are investigated. The model highlights the relative impact of each transport mechanism on delivery, showing that binding and surface erosion can be used in a diffusion model to fit early burst release and later prolonged release phases simultaneously. A similar model is used to simulate transdermal delivery, incorporating diffusion, epidermal turnover and slow equilibration processes. It is shown that the presence of slow binding events in the stratum corneum can enhance the effect of epidermal turnover on in vivo delivery. Fitting to experimental data for theophylline found in the literature shows that epidermal turnover may affect smaller, more hydrophilic drugs than previously believed due to slow binding. It is shown that this could be an important contribution to the discrepancy between in vitro and in vivo data often observed. A two-dimensional finite element model is developed in Python to investigate the effect of lipid layer structure and cornified envelope permeability on permeation pathways. It is shown that a realistic depiction of lipid phase anisotropy leads to a higher contribution of intercellular transport than predicted by previous models of lipid anisotropy. Limited cornified envelope permeability is investigated as an alternative method for simulating the effects of anisotropic diffusion.