This paper investigates the connection between past tense and modality in six Romance and Germanic languages (French, Italian, Spanish, Dutch, English and German). I first argue for an aspecto-temporal definition of imperfects and preterits based on the notion of 'reference point' (R) and I suggest that the different interpretations of past tenses (including the modal ones) reflect specific instantiations of R as 'topic time', 'aspectual vantage point' or 'epistemic evaluation'. Second, I offer a classification and analysis of the modal uses of the imperfects and preterits observed in the languages under investigation. Finally, I expand on the idea that the modal interpretations of past tenses correspond to pragmatic inferences that are being conventionalised and mirror the stages of 'bridging contexts' and 'switch contexts' described in Heine's (2002) model for semantic change.