As universities in the United Kingdom gear themselves up for the next Research Excellence Framework, REF2021, with peer review at its core, we critically re-visit the idea of peer review as a gold standard proxy for research excellence. We question the premise that anonymous peer review is a necessary and enabling condition for impartial, expert judgement. We argue that the intentions and supposed benefits underlying peer review and its associated concepts have become congealed in received discourse about research quality. Hence we explore the key conceptual issues raised by the nested assumptions and concepts that come into play in peer review as currently practised: primarily those of secrecy, anonymity, legitimacy, trust, impartiality and openness. After delineating the benefits attributed to peer review, we contrast its declared virtues with its problematic features. We locate peer review in an audit culture in which the reviewer is an academic labourer. Drawing on recent trends in moral and political philosophy, we question the usefulness of the ideal of impartiality when tied to secrecy. Then we raise more deliberative, intersubjective possibilities for a revised understanding of peer review in the context of an academic community. Finally, we suggest ways in which the academic community could pursue quality in research by recasting peer review to be less secret and more open.