In the first place, this paper shows that utterances with focus take different meanings at odds with a unitary definition of focus. These meanings fall into three main areas: identification, explanation and intensive exclamation. A new definition of focus is then put forward, as a specific mode of identification: assertion consists in the qualitative designation of an element whose existence is pre-asserted. This analysis accounts for the different meanings of focus-markers, through a regular mechanism which relates the utterance to the different contexts locating it. Various structures expressing focus in different languages are consequently accounted for, together with various related syntactic or semantic problems: aspecto-temporal conditioning, restrictive agreement, dependancy, correlation with nouns...