An Independent Supervisory Authority has several responsibilities.

It is up to a supervisory authority to inspect and take measures to compel companies to conform to the GDPR.

According to paragraph 1 of Article 51.

1. 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’).

Chapter VI of the GDPR talks about laws on independent supervisory authorities.