This article examines how the EU legal frameworks on copyright, database, and computer programs restrict the application of text and data mining technology (TDM) in the European Union (the EU). The paper analyzes the sufficiency of TDM exceptions of the EU Directive on copyright and related rights in the Digital Single Market (the DSM Directive) in the context of the development of Artificial Intelligence (AI). The paper indicates that national transposition is one of the possible ways to improve the TDM exceptions. The EU Member States had until 7 June 2021 to transpose the DSM Directive into their national laws. However, the implementation process appears to be far from complete. Therefore, the article considers the positions of the EU Member States, which have already implemented the new legal framework into their national laws, regarding the scope of TDM exceptions. In particular, the paper analyses whether issues that have been unclear since the adoption of the DSM Directive have been covered adequately through the transposition process. Finally, this paper puts forward recommendations on how it could be implemented to unlock the maximum potential of TDM and AI research in the EU.