Compliance with the GDPR is monitored by the national data protection authorities (DPAs). DPAs can conduct investigations and impose sanctions where necessary. DPAs have a number of tools at their disposal, including fines up to 20 M€ or 4% of the worldwide annual turnover whichever is higher, reprimands, and temporary or permanent processing bans.
You can find the contact details for all EEA DPAs on the EDPB website: Members
More information: