This fourth volume of the series "Progress in Physical Chemistry" is a collection of mini-review articles written by those who were project leaders and members of the Collaborative Research Centre (SFB) 458 of the German Research Foundation (DFG). The articles are based on ten years of intense coordinated research and report particularly on the scientific progress made at SFB 458 since 2005. Their common theme is the study of ionic motion in disordered materials over wide scales in space and time. The mini reviews thus address key questions in the rapidly developing field of SOLID STATE IONICS, a discipline which has its roots in the physics and chemistry of solids and is now a thriving branch of materials science and engineering. In the materials studied, the dynamics of the mobile ions are de-termined by disorder and interaction. This complicated many-particle problem constitutes an area of basic research in its own right. At SFB 458, it has been tackled on complementary routes, i.e., by synthesis of new disordered electrolytes, by advanced experimental techniques and by numerical simulations and model concepts. Substantial progress has thus been made in developing a coherent view and a new understanding of the ionic motion in materials with disordered structures.