The European Union Artificial Intelligence Act (AIA) is the first wholesale attempt by a major regulator to legislate AI. In adopting its proposal for the AIA, the European Commission recognised that the use of AI can adversely affect a number of fundamental rights enshrined in the EU Charter of Fundamental Rights. The AIA adopts a risk-based approach, whereby stricter rules are applied depending on the risk categorisation of the AI system. This talk will explore how the AIA seeks to protect fundamental rights through its risk-based approach, with a particular focus on the rights to respect for private life and protection of personal data (Articles 7 and 8), the freedom of expression (Article 11) and non-discrimination (Article 21). This talk will consider alternative approaches to AI governance seen in the United States, the UK and China, and will evaluate whether the AIA meets the objectives of the Commission in ensuring that AI systems placed on the Union market respect existing laws on fundamental rights.