This review represents the authors' view of the evolution of solid-state ionics over approximately the past 100 years. A brief history, introducing milestones of the development of this discipline, is followed by a short summary of the theory of ionic conduction in the bulk and the more recently developed theory of ionic conduction at interfaces. The central part of the article gives examples of ionic-conducting materials systems with structures ranging from one- to three-dimensional disorder. Important experimental techniques for analyzing ionic conduction, including alternating-current impedance spectroscopy, direct-current coulometry, and direct-current current-voltage measurements with blocking electrodes, are also summarized. The main technological applications, that is, batteries, solid-oxide fuel cells, electrochemical sensors, electrochromic windows, and oxygen-separation membranes, are reviewed. Finally, new concepts in solid-state ionics are presented, including the investigation of new materials (such as nanostructured phases), the study of boundaries (for example, using microelectrodes), the development of computational techniques, and the connections with other classes of materials (notably magnetic and semiconducting materials).