The main research funders in Europe are supporting Open Science principles and practices, and researchers are required to follow some policies, but what about the research institutions? Are they ready to support those principles and practices? Are they providing tools and services for their researchers? Are they acknowledging and rewarding Open Science in the same way they have been assessing research until now? In this talk we will review which are the main challenges that a research institution must face in relation to Open Science. As it will be seen, it is not enough to promote open access to publications and to facilitate research data sharing. Institutions need to make a cultural change in the way research is performed and assessed. And the change must affect any other academic activity beyond research.