Diffraction techniques - incorporating both x-rays and neutrons, single-crystals and powders - have been developed to allow crystal structures to be determined at high pressures with high accuracy. For single-crystal neutron-diffraction studies, an optimised data collection strategy has been developed for use with a sapphire-anvil pressure cell and a position-sensitive detector and, combined with a newly developed clamp-type pressure cell, has allowed both the scope and accuracy of high-pressure structural studies using neutron-diffraction techniques to be extended. Application of the new techniques to high-pressure structural studies of H-ordering systems of the KH₂PO₄-type, strongly suggests that the H-atom site separation, δ, is a strong determinant of the ordering temperature T_c such that a hydrogenous material and its deuterated analogue have the same T_c, within error, at the same δ. The results also suggest that the differences in T_c between different H-ordering systems are determined by the differences in δ, and that δ in all systems tends to im0.22pr and T_{c→OK. For single-crystal x-ray diffraction studies using a diamond-anvil cell, analysis has shown that removal of intensity from either the incident or diffracted beams by simultaneous diffraction of the diamonds can reduce the intensity of sample reflections by up to 50%. A data collection strategy to detect this effect has been developed. The use of tungsten as a gasket material has also been investigated, and provides a possible solution to the long-standing problem of using AgK}α radiation for single-crystal studies. Application of these newly-developed techniques to a structural study of the high-T_c superconductor YBa₂Cu₄O₈, illustrates the improved accuracy now available using single-crystal x-ray diffraction techniques and AgKα radiation. The results of this study cast considerable doubts on the accuracy of previous high-pressure structural studies of high-T_c superconductors. Work has also been done on developing powder-based techniques. These show considerable promise for accurate structural studies to very high pressures in the future.