The European Commission proposed harmonised rules on artificial intelligence (AI) on the 21st of April 2021 (namely the EU AI Act). Following a consultative process with the European Council and many amendments, a General Approach of the EU AI Act was published on the 25th of November 2022. The EU Parliament approved the initial draft in May 2023. Trilogue meetings took place in June, July, September and October 2023, with the aim for the European Parliament, the Council of the European Union and the European Commission to adopt a final version early 2024. This is the first attempt to build a legally binding legal instrument on Artificial Intelligence in the European Union (EU). In a similar way as the General Data Protection Regulation (GDPR), the EU AI Act has an extraterritorial effect. It has, therefore, the potential to become a global gold standard for AI regulation. It may also contribute to developing a global consensus on AI Trustworthiness because AI providers must conduct conformity assessments for high-risk AI systems prior to entry into the EU market. As the AI Act contains limited guidelines on how to conduct conformity assessments and ex-post monitoring in practice, there is a need for consensus building on this topic. This paper aims at studying the governance structure proposed by the EU AI Act, as approved by the European Council in November 2022, and proposes tools to conduct conformity assessments of AI systems.