Text and Data Mining (hereinafter, TDM) issue for the purpose of scientific research or for any other purpose which is included in the provisions of the new EU Directive on Copyright in the Digital Single Market (hereinafter, DSM). TDM is a term that includes Web harvesting and Web Archiving activities. Web harvesting and archiving pertains to the processes of collecting from the web and archiving of works that reside on the Web. Web harvesting and archiving is one of the most attractive applications for libraries which plan ahead for their future operation. When works retrieved from the Web are turned into archived and documented material to be found in a library, the amount of works that can be found in said library can be far greater than the number of works harvested from the Web. This paper aims at presenting certain issues related to the existing legal framework as well as technical/librarianship issues that apply to TDM which includes Web harvesting and archiving activities. This paper elaborates upon the applicable new provisions of Directive 2019/790/EU on Copyright in the DSM with the aim to shed light upon issues such as the notion of “lawful access”, the beneficiary of the mandatory exception for TDM, the purpose-specific TDM described in art. 3 of the new Directive on Copyright in the DSM, and the application of the “three-step test” in TDM.