The history of the high-field domains is given with the description of the experimental and theoretical results of the team of the author in the first decade after their discovery in 1958. This work is done at CdS single crystal platelets that are used as a model substance. The major findings of modern high-field domain research that followed their original research are then reviewed. It is emphasized that all high-field domains are created for reasons of the minimum entropy production principle when the conductivity decreases more than linear within a semiconductor. The application of these high-field domains in important semiconductor devices are reviewed that have now reached a multibillion dollar market.