In crystalline, glassy and molten electrolytes, the dynamics of the mobile ions is best studied by taking conductivity spectra, i.e., by measuring ionic conductivities in the entire range from de to far-infrared frequencies. Experimental conductivity spectra are reviewed and discussed, with particular emphasis on their high-frequency plateaux and their low-frequency scaling properties. The concept of mismatch and relaxation (CMR) is shown to provide a general basis for understanding the spectra in terms of the ion dynamics. The conductivity spectra of crystalline fast ion conductors are, e.g., explained by the jump relaxation model, which builds on the CMR. In glassy electrolytes, the mobile ions encounter different kinds of site, and the jump relaxation model has to be modified accordingly. Formulating the CMR without reference to the existence of fixed sites yields a description of the ion dynamics in simple molten salts. The model is thus able to reproduce both the conductivity spectra of fragile molten salts and the characteristic temperature dependence of their de values. The remarkable low-frequency scaling behaviour of glassy electrolytes is considered a manifestation of the particular long-time properties of the CMR.