Recent progress in the theoretical understanding of fast ion conduction in solids is discussed, with emphasis placed on mechanistic behavior and on the characteristic features of particular sorts of solid electrolytes. We consider soft framework materials such as α-AgI, and hard framework materials such as β″-alumina. In each case, we discuss which theoretical methods have been used to investigate mechanisms of conductivity and diffusion, and some of the physical insights which have been gleaned on the mechanism of ionic conductivity. Comments are also made on glassy conductors such as glassy lithium aluminosilicate, and polymeric ionic conductors such as polyethylene oxide/lithium triflate. Since different characteristic timescales, and characteristic energies, are appropriate for these different classes of materials, varying theoretical methods have been used, and should be used, to understand the ionic motion. Particular concepts, such as dynamic percolation in polymer electrolytes, strong memory effects in soft framework materials, strongly correlated liquid-like diffusion in hard framework materials and disorder-induced weadening of correlations in glassy materials are pointed out. We speculate briefly on the role of very strong interionic correlations in causing possible domain-wall conduction, a process that goes well beyond any hopping description. We briefly discuss some special behavior observed in certain classes of solid electrolytes, such as fractal behavior, "universal dielectric response", the mixed alkali effect in glasses, and the "Liang effect", which is the enhancement of ionic conductivity by inclusion of an insulating second phase. Remarks are ventured both on theoretical methodology and on the usefulness of models for understanding, predicting and designing solid electrolyte behavior.