To describe experimental results on magnetic orderings in erbium, the model was introduced in 1961 by Roger Elliott from the University of Oxford. The model has given its name in 1980 by Michael E. Fisher and Walter Selke, who analysed it first by Monte Carlo methods, and then by low temperature series expansions, showing the fascinating complexity of its phase diagram, including devil's staircases and a Lifshitz point. Indeed, it provides, for two- and three-dimensional systems, a theoretical basis for understanding numerous experimental observations on commensurate and incommensurate structures, as well as accompanying phase transitions, in various magnets, alloys, adsorbates, polytypes, multiferroics, and other solids. Further possible applications range from modeling of cerebral cortex to quantum information.