Norman Fairclough's books, Language and Power (1989) and Critical Discourse Analysis (1995), articulate a three-dimensional framework for studying discourse, "where the aim is to map three separate forms of analysis onto one another: analysis of (spoken or written) language texts, analysis of discourse practice (processes of text production, distribution and consumption) and analysis of discursive events as instances of sociocultural practice" (1995: 2).
In addition to linguistic theory, the approach draws from social theory--and contributions from Marx, Gramsci, Althusser, Habermas, and Foucault--in order to examine ideologies and power relations involved in discourse. Fairclough notes "that language connects with the social through being the primary domain of ideology, and through being both a site of, and a stake in, struggles for power" (1989: 15).
Notable researchers include Norman Fairclough, Paul Chilton, Teun van Dijk, Christina Shaffner, Ruth Wodak, Peter Teo, Roger Fowler, Gunther Kress, and Robert Hodge.