Current transfer behaviour in anisotropic superconducting bodies is the central topic of this thesis and focuses on the effect that the nonlinearity of the electric field dependence upon the local current density value and anisotropy have on the nature of current transport. The main motivation for this work was the desire for a better understanding of the conceptually difficult behaviour of current transport in superconducting bodies and examines current transfer quantitatively for a number of important problems on the macroscopic and microscopic scale. This behaviour is examined both experimentally and using computer models. The successful development of a powerful, robust and adaptable numerical model for analysing the complex current transfer behaviour has been the primary aim of this work. The range of parameters appropriate to macroscopic models of the Bi-2212 CRT system has been experimentally examined using a specifically constructed apparatus for the measurement of current transport characteristics. A study of the self-field properties of the Bi-2212 CRT material using a new experimental technique and mathematical analysis is presented and has allowed the importance of the self-field effect in the numerical model to be assessed. An essential requirement for the practical application of high current superconducting devices is the development of low resistance current contacts. The research presented examines this macroscopic current transfer problem and aims to explain experimentally observed current transfer characteristics at high applied currents. Existing models cannot explain these characteristics. Current transfer on the microscopic scale is also examined. Models of current transfer have been developed from descriptions of specific microstructures that are thought to characterise the microstructure of Bi-2223 and Bi-2212 silver-sheathed tapes. This thesis specifically presents modelling of current transfer between c-axis, low-angle c-axis and edge-on c-axis tilt oriented grain interfaces; the principal current transfer paths between individual current elements of the microstructural models of current flow in polycrystalline HTSs.