This volume addresses problems of semantics regarding the analysis of tense and aspect (TA) markers in a variety of languages, including Arabic, Croatian, English, French, German, Russian, Thai, and Turkish. Its main interest goes out to epistemic uses of such markers, whereby epistemic modality is understood as indicating “a degree of compatibility between the modal world and the factual world” (Declerck). All contributions, moreover, tackle these problems from a more or less cognitive point of view, with some of them insisting on the need to provide a unifying explanation for all usage types, temporal and non-temporal, and all of them accepting the premise that the semantics of TA categories essentially refers to subjective, rather than objective, concerns. The volume also represents one of the first attempts to gather accounts of TA marking (in various languages) that are explicitly set within the framework of Cognitive Grammar. Ultimately, this volume aims to contribute to establishing an awareness that modal meaning elements are directly relevant to the analysis of the grammar of time.