This paper examines two cognitively-based models of text comprehension and suggests how these might be combined, and integrated with a functional grammar in order to provide an overall model which takes us from a structured sequence of words to the understanding of the concepts conveyed. The paper first provides illustrated summaries of Kintsch’s construction-integration model and Werth’s text world model. Discussion of their similarities and differences suggests that they are not incompatible, but that both lack a suitable grammatical component. The paper then examines the properties which such a grammar needs to have, and demonstrates that Role and Reference Grammar is an appropriate choice. The parts of the model are then brought together in relation to a short but complete text taken from a corpus. The paper is rounded off with some concluding remarks.