Evidentiality or, following the French linguistic tradition, “mediativity” is a complex and controversial category, with an already extensive body of literature devoted to other languages and a few studies focusing on Portuguese. As a conceptual category, abstracting away from its linguistic means of expression, which is to some extent present in languages such as Portuguese that lack a specific grammatical system for its codification, evidentiality/mediativity raises two main issues which are yet to be addressed: the first question concerns the definition of its status as a grammatical, semantic or discursive category and of its conceptual basis, traditionally characterized as referring to the source of information for the propositional content of the utterance, while the second touches upon its demarcation with respect to the conceptual category of epistemic modality. The aim of this study is to provide an answer to both questions from a cognitive-functional, usage-based perspective, on the basis of two grammaticalized evidential/mediative markers of Portuguese, namely the compound form of the future and the verb parecer ‘seem’ followed by a non-finite verb or a finite clause. We sustain the view that evidentiality provides an indication about the source and reliability of the information, and that reliability does not necessarily involve degrees of epistemic speaker commitment or degrees of (un)certainty. While the reportative evidential uses of the compound form of the future in Modern European Portuguese, typical of news reports, and of parecer provide evidence for the relative independence of evidentiality in relation to epistemic modality, the inferential evidential uses of the compound future and of parecer reveal a close link, and even a partial overlap, between evidentiality and epistemic modality. Both reportative and inferential uses of these evidential markers contribute to the speaker’s epistemic control in the discourse and speaker’s intersubjective alignment. While the inferential uses of the compound future and of parecer stemmed from diachronic cognitive and pragmatic-discursive processes of subjectification, the reportative uses of these evidential markers resulted from diachronic cognitive and pragmatic-discursive processes of intersubjectification.