Each member state in the EU has a data protection authority (DPA), which is used synonymously with supervisory authority in the GDPR regulation text. The DPA oversees the application of data protection relevant to GDPR in their respective member states. They also act as the primary liaison for the member states and the EU.
Supervisory authority is mentioned over 200 times in the GDPR and has the general description: “Each Member State shall provide for one or more independent public authorities to be responsible for monitoring the application of this Regulation, in order to protect the fundamental rights and freedoms of natural persons in relation to processing and to facilitate the free flow of personal data within the Union (‘supervisory authority’).”
Articles 51 through 67 define and spell out the responsibilities of the supervisory authority, which is the DPA of each EU member state. In addition to overseeing the application and enforcement of GDPR in their member states, each DPA also participates in the European Data Protection Board.