The current range and volume of research evaluation-related literature is extensive and incorporates scholarly and policy/practice-related perspectives. This reflects academic and practical interest over many decades and trails the changing funding and reputational modalities for universities, namely increased selectivity applied to institutional research funding streams and the perceived importance of university rankings and other reputational devices. To make sense of this highly diverse body of literature, we undertake a critical review of over 350 works constituting, in our view, the 'state-of-the-art' on institutional performance-based research evaluation arrangements (PREAs). We focus on PREAs because they are becoming the predominant means world-wide to allocate research funds and accrue reputation for universities. We highlight the themes addressed in the literature and offer critical commentary on the balance of scholarly and policy/practice-related orientations. We then reflect on five limitations to the state-of-the-art and propose a new agenda, and a change of perspective, to progress this area of research in future studies.