The implementation of policies promoting the adoption of an Open Science culture must be accompanied by indicators that allow monitoring the penetration of such policies and their potential effects on research publishing and sharing practices. This study presents indicators of Open Access (OA) penetration at the institutional level for universities worldwide. By combining data from Web of Science, Unpaywall and the Leiden Ranking disambiguation of institutions, we track OA coverage of universities’ output for 963 institutions. This paper presents the methodological challenges, conceptual discrepancies and limitations and discusses further steps needed to move forward the discussion on fostering Open Access and Open Science practices and policies.