Grain boundaries form the basis of an important Josephson junction technology in the cuprates and also limit the superconducting critical currents attainable in practical, polycrystalline materials. An improved understanding of these defects is therefore important for applications. The status of the current understanding of cuprate grain boundaries is summarised and experimental investigations are presented, focusing on the less well understood high angle boundaries. Measurements of the capacitance of grain boundaries in the overdoped superconductor Y1-xCaxBa2Cu3O7-8, were performed as a function of the calcium content, using the Josephson coupling across the boundaries. Particular care was taken to eliminate the e ects of heating and stray capacitance due to the substrate. The e ect of thermal noise was also assessed. These measurements provide important information about the area and the width of the grain boundaries, that highlights their inhomogeneous nature. A new technique was applied to measure the normal state properties of YBa2Cu3O7-8 grain boundaries above the critical temperature. Since the resistance of the adjacent material at high temperatures is comparable to, or greater than that of the grain boundary, a compensating Wheatstone bridge structure was used. The errors involved in this technique are carefully assessed and quanti ed. The normal state resistance of a number of di erent grain boundary orientations was measured from room temperature to the critical temperature. Detailed characterisation of the grain boundaries, including measurements of the critical current and the current voltage characteristics at low temperatures, was performed. The results obtained are used to assess the validity of the various theories for the grain boundary electrical structure. A tunneling model that accounts for the band structure of the material is developed and applied to potential barriers consistent with a band bending model. This theory is shown to provide a convincing account of the experimental results presented in this thesis.