Superionic conductors are compounds that exhibit exceptionally high values of ionic conductivity within the solid state. Indeed, their conductivities often reach values of the order of 1 −1 cm −1 , which are comparable to those observed in the molten state. Following Faraday's first observation of high ionic conductivity within the solids β-PbF 2 and Ag 2 S in 1836, a fundamental understanding of the nature of the superionic state has provided one of the major challenges in the field of condensed matter science. However, experimental and theoretical approaches to their study are often made difficult by the extensive dynamic structural disorder which characterizes superionic conduction and the inapplicability of many of the commonly used approximations in solid state physics. Nevertheless, a clearer picture of the nature of the superionic state at the ionic level has emerged within the past few decades. Many different techniques have contributed to these advances, but the most significant insights have been provided by neutron scattering experiments and molecular dynamics simulations. This review will summarize the state of current knowledge concerning the crystal structures and conduction processes of superionic conductors, beginning with a comparison of the behaviour of two of the most widely studied binary compounds, AgI and β-PbF 2 . Each can be considered a parent of two larger families of highly conducting compounds which are related by either chemical or structural means. These include perovskite-structured oxides and Li + containing spinel-structured compounds, which have important commercial applications in fuel cells and lightweight batteries, respectively. In parallel with these discussions, the relative importance of factors such as bonding character and the properties of the mobile and immobile ions (charge, size, polarizability, etc) in promoting the extensive lattice disorder which characterizes superionic behaviour will be assessed and the possibilities for predicting a priori which compounds will display high ionic conductivity discussed.