A number of basic scientific questions relating to ion conduction in homogeneously disordered solids are discussed. The questions deal with how to define the mobile ion density, what can be learned from electrode effects, what is the ion transport mechanism, the role of dimensionality, and what are the origins of the mixed-alkali effect, of time-temperature superposition, and of the nearly-constant loss. Answers are suggested to some of these questions, but the main purpose of the paper is to draw attention to the fact that this field of research still presents several fundamental challenges.

A model for ion transport in glass is presented which is based on the experimental evidence that cations in glass create and maintain their own characteristic environments. By postulating the existence of a site memory effect, we are able to visualize the formation of conducting pathways. We develop a quantitative theory which explains the general occurrence of the mixed cation (alkali) effect in glassy material and, in addition, shows that the anomalous dependence of conductivity on the modifier content in single alkali glasses follows a simple power-law relation.

We discuss examples of complex systems composed of many interacting subsystems. We focus on those systems displaying nontrivial long-range correlations. These include the one-dimensional sequence of base pairs in DNA, the sequence of flight times of the large seabird Wandering Albatross, and the annual fluctuations in the growth rate of business firms. We review formal analogies in the models that describe the observed long-range correlations, and conclude by discussing the possibility that behavior of large numbers of humans (as measured, e.g., by economic indices) might conform to analogs of the scaling laws that have proved useful in describing systems composed of large numbers of inanimate objects

We perform Monte Carlo simulations for diffusion of charged particles in structurally disorderd lattices. As a consequence of the Coulomb interaction, pronounced backward correlations occur which lead to power-law behavior of the relevant transport quantities at intermediate time and frequency scales. Both the exponents and the size of the dispersive regime depend on temperature. Our simulations suggest that the combined effect of disorder and Coulomb interaction provides a new mechanism for understanding non-Debye relaxation, which is experimentally known for a wide class of materials.