Europe’s incoming Directive on Copyright in the Digital Single Market contains two new exceptions allowing text and data mining (TDM). The Directive is currently being implemented by all member states and must come into force no later than June 2021. Article 3 grants universities, educational establishments and libraries the right to mine in-copyright works to which they have lawful access, and Article 4 introduces an exception mainly aimed at commercial data analytics and AI. This second exception could be helpful in the context of Knowledge Transfer between private companies and universities. Although a few European countries already have copyright exceptions for TDM, the majority do not. This means that most European research librarians and libraries need to start considering how they can best use this exciting new opportunity to support researchers undertaking TDM. Meanwhile, libraries who have already benefited from a TDM exception need to think how best to bridge the gap between the existing exception and the new TDM exceptions. This document contains several recommendations for libraries in both categories, who want to strengthen their TDM capacity.