Abstract The article presents a theoretical reflection on research evaluation regimes – state-initiatives historically installed in European countries to coordinate the distribution of research funding – and proposes four dimensions enabling their comparison from a global perspective and potentially advancing future research. We take Michael Power’s argument that evaluations are cultural artefacts and essentially linked to modes of governing as a starting point to further the analytical reflection on the modes of governing science through research evaluation regimes and develop a critical heuristic that accounts for so far neglected aspects. Much of the existing scholarship on research evaluation systems adopts a case-based approach shaped by methodological nationalism, thereby neglecting transnational processes, historical and socio-political variation, and the diverse constellations of formal and informal relationships between evaluating and evaluated actors. Based on this critique, we develop a heuristic of four dimensions of research evaluation regimes which can inform future research on transnational dynamics and normative aspects. The article identifies the constellation of actors (1), procedures (2), functions (3), and programmes and values (4) as core dimensions of research evaluation regimes which can advance inquiries into the governing of science through research evaluation from a transnational perspective. The heuristic is presented as a starting point to conduct context-sensitive, comparative studies of research evaluation regimes and their governing of science.