Abstract This paper briefly introduces some basic notions of cognitive grammar. It emphasizes the importance to linguistic semantics of the way in which we ‘construe’ a conceived situation, and explores the reasons why the nature of the construals we impose are largely ‘invisible’ to us. They can, however, be made visible by the careful analysis of linguistic data. Several examples are given of constructs useful for semantic description which first become apparent from the attempt to explicitly characterize particular grammatical constructions. It is concluded that developing an optimal account of semantic structure and an optimal account of grammatical structure are best conceived as simultaneous, mutually informative enterprises.