Processing an utterance involves identifying the time - past, present or future - at which the event described in that utterance is meant to be located. This identification exploits the interaction of the tense system of the language with other syntactic, semantic and pragmatic variables. It is claimed that the basic 'default' meaning of the tense markers of English can be overruled by purely lingustic means, by contextual means, or by a combination of the two. These possibilities are illustrated by making crucial use of the notion of relevance developed recently by Sperber & Wilson. In addition to examples of the many-many relations of times and tenses, there are tentative analyses for conditionals and the perfect. Finally the implications of these analyses for the traditional Chomskyan notions of grammaticality and acceptability are discussed.