This paper discusses the role played by cognition in three linguistic theories which may be labelled as "structural-functional": Functional (Discourse) Grammar, Role and Reference Grammar and Systemic Functional Grammar. It argues that if we are to achieve true cognitive adequacy, we must go well beyond the grammar itself to include the processes of conceptualisation, categorisation and construal, and that the model should be dynamic, in the sense that it should describe the processes of language production and comprehension rather than only the patterns found in languages. The discussion provides evidence that none of the three theories can currently be considered to achieve high standards of cognitive adequacy, despite the efforts made in this direction in Functional Discourse Grammar. Recent work which links Role and Reference Grammar to studies of production and comprehension is, however, promising. The paper ends with a plea for a more highly developed synthesis of work in linguistics, psycholinguistics, cognitive psychology, neurology and neurolinguistics, integrated with perspectives from the study of the sociocultural contexts in which language is used. (Contains 1 figure.)