This collaborative paper looks at how libraries can engage with and offer leadership in the Open Science movement. It is based on case studies and the results of an EU-funded research project on Research Data Management taken from European research-led universities and their libraries. It begins by analysing three recent trends in Science, and then links component parts of the research process to aspects of Open Science. The paper then looks in detail at four areas and identifies roles for libraries: Open Access and Open Access publishing, Research Data Management, E-Infrastructures (especially the European Open Science Cloud), and Citizen Science. The paper ends in suggesting a model for how libraries, by using a 4-step test, can assess their engagement with Open Science. This 4-step test is based on lessons drawn from the case studies.