In order to demonstrate compliance with the GDPR, the data controller or data processor should maintain records of processing activities under its responsibility. Each data controller and data processor should be obliged to cooperate with the supervisory authority and make those records, on request, available to it, so that it might serve for monitoring those processing operations (Recital 82).
If you are a Data Processor as opposed to a Data Controller, you still have recording obligations but less. See Processing Records Database (excel) (Data Processor)
