Earthing systems are designed to perform satisfactorily under normal system voltage conditions as well as power frequency faults. The performance of most earth electrode geometries is now fairly well understood under these conditions. However, the response of earthing systems under high frequency and transient conditions is yet to be fully clarified, and there are several aspects of earthing systems that require further investigations. In this thesis, both modelling and experimental studies were carried out using high frequency and impulse current injection. Generic earth electrodes as well as the full earthing grid of an operating substation were investigated. The studies carried out in this work have confirmed some of the previous findings published in the open literature, and have clarified some aspects of conduction in earthing systems. The literature review on injuries due to lightning currents has highlighted the importance of good earthing systems. A comprehensive parametric simulation study was conducted on vertical rods, horizontal electrodes as well as earth grids under variable frequency and impulse currents. The effects of geometry and soil characteristics were also studied. It was demonstrated that significant inductive effects appear at high frequency, and the size of the earthing systems was found to reach an "effective dimension" beyond which negligible performance benefit is obtained. For horizontal electrodes the concept of effective length is investigated and for grids the effective area was used instead. The Simulation techniques developed for these simple electrodes were applied to an operating transmission substation, and similar trends were seen under high frequency and impulse current conditions. The safety voltages were calculated but no conclusion could be drawn as there are no recommended safety guidelines for safety at high frequency and impulse current. These Generic studies have led to a new proposal for earthing systems so that the short fall of poor performance due to inductive effects and "effective dimensions" are minimized. It was shown that this proposal is a major improvement on the existing enhancement techniques currently used in practice. Parallel to the simulation programme, an experimental set up was used to study the performance of laboratory earth electrode models under fast impulse current. It was found that highly non-linear conduction phenomena take place in such configurations. These complex conduction processes were explained by thermal effects and soil ionisation.