It was founded by Louis Hjelmslev (1899–1965) and Viggo Brondal (1887–1942). In the mid twentieth century the Copenhagen school was one of the most important centees of linguistic structuralism together with the Geneva School and the Prague School. Together they founded the Cercle Linguistique de Copenhague a group of linguists based on the model of the Prague Linguistic Circle.
Hjelmslev’s more formalist approach attracted a group of followers, principal among them Hans Jorgen Uldall and Eli Fischer Jorgensen, who would strive to apply his abstract ideas of the nature of language to analyses of actual linguistic data. Hjelmslev’s objective was to establish a framework for understanding communication as a formal system, and an important part of this was the development of precise terminology to describe the different parts of linguistic systems and their interrelatedness. The basic theoretical framework, called “Glossematic” was laid out in Hjelmslev’s two main works: Prolegomena to a theory of Language and Résumé of a theory of Language. However, since Hjelmslev's death in 1965 left his theories mostly on the programmatic level.
In 1989, a group of members of the Copenhagen Linguistic Circle, inspired by the advances in cognitive linguistics and the functionalist theories of Simon C. Dik founded the School of Danish Functional Grammar aiming to combine the ideas of Hjelmslev and Brøndal, and other important Danish linguists such as Paul Diderichsen and Otto Jespersen with modern functional linguistics. Among the prominent members of this new generation of the Copenhagen School of Linguistics were Peter Harder, Elisabeth Engberg Petersen, Frans Gregersen and Michael Fortescue. The basic work of the school is Dansk Funktionel Grammatik (Danish Functional Grammar) by Harder (2006).