This review represents the author's view of the evolution of solid-state ionic studies in Niigata University over the past 50 years. A brief history, starting from the caterpillar mechanism theory, is followed by a short summary of the theory of electric conduction and diffusion in both ionic and electronic mixed conductors. The cross-conductivity experiments in Ag2X (X=chalcogen) and the tracer technique for investigating the deviation from the Einstein relation are followed. In the middle part of the article, the more recently developed theoretical works on the electronic states of noble metal halides and alkali halides are given. These theoretical works have brought more microscopic evidence for the p-d hybridization in noble metal halides. Causality, stability and fractal are fundamental concepts in condensed matter physics. Next, investigations on a causality breaking found in ionic materials are followed. Lastly, design studies of new materials with high functions, such as high ionic conductivity, high diffusion coefficient, etc., are introduced. Computer simulations by a molecular dynamics method have been performed to a model material, for example, which is composed of accumulating two different fluoride conductors:(BaF2)-Ba-...-CaF2-BaF2-CaF2(...). (C) 2004 Elsevier B.V. All rights reserved.