This paper aims to describe a research project focused on the digital representation of information related to the privacy and data protection domain. Currently, privacy policies are used by data controllers as a tool to achieve compliance with data protection regulations such as the EU GDPR, instead of being a privacy instrument at the disposal of both controllers and data subjects. On the other hand, data subjects lack the tools to effectively establish preferences when it comes to the processing and disclosure of their personal data, as well as to easily exercise their rights. In this regard, this paper discusses the challenges of the implementation of a service based on decentralised Web technologies and Semantic Web standards and specifications to facilitate the communication between data subjects and data controllers in the light of the GDPR. The main challenges that this service intends to address are linked to the exercising of GDPR-related rights and obligations, the negotiation of privacy terms and the governance of access to personal data stores. A case study in the healthcare and genomics domain will be explored to experiment with the developed tools. Early-stage results related to the implementation of semantic policies for the representation of GDPR rights and obligations are presented.