Peer review is primarily discussed in the literature with respect to its deficits, e.g. bias or inefficiency. In contrast, our synthesis asks why peer review is used ubiquitously and why it works despite such deficits. Historically, one answer lies in peer review not just providing expertise-based decisions on scientific resources (publication space, funding, jobs), but also providing an organized procedure to give these decisions legitimacy outside of science, e.g. in politics. The current situation is marked by a landscape of national and international funding and review activities that not only complement each other, but overlap, mirror, or rival each other. The current challenge rests in adapting peer review to different funding programmes within this landscape and without adding unnecessary burden on researchers and research organisations. To capture these aspects of scientific self-governance, we suggest an alternative conception of grant peer review that allows for thinking about peer review procedures as made up of different elements. Our key findings from such a conception are the following:- Peer review procedures have become more complex and formalized, as a result of being adapted to the different settings in publishing, funding, and hiring, on the national and international level. - The diversity and ubiquity of peer review rests upon its adaptability and scalability in reaching the ‘right’ decisions, i.e. based on scientific exellence, as well as in producing legitimate decisions, i.e. accepted by multiple stakeholders.- Peer review can be partitioned into eight elemental practices: four essential practices – postulating, consultative, decisive, and administrative – and another four – debating, presenting, observing, and moderating – that provide further combinatorial possibilities.- Through context-specific combinations of these elemental practices into a procedure, peer review generates legitimacy for judgements on scientific quality, inside and outside of science.- Peer review should not be seen as a 'measurement device' for scientific quality. Its diversity attests to the fact that issues of quality and legitimacy are intertwined and should be addressed openly.- Peer review procedures can act as laboratories for deliberation where the robustness and validity of research are equally relevant issues as participation, representation, accountability, or legibility; in effect, allowing for experiments and innovations in science policy.