With the Artificial Intelligence Act (AI Act), the European Union has drafted a pioneering piece of legislation aiming to regulate the variety of jeopardies AI systems can pose to its citizens, especially concerning the use of AI in surveillance. This thesis examines the problems caused by the usage of AI in facial recognition technologies (FRTs) comprising of e.g., fundamental rights violations regarding the collection of biometric data of individuals and the discrimination through biased outputs or technological inaccuracies by the respective AI systems as well as the methods and mechanisms applied by the AI Act in order to address those issues. In this context, the risk-based approach of the AI Act, which categorizes most FRTs as either a prohibited AI practice or as high-risk AI, and the prohibition on the use of real-time remote biometric identification systems in publicly accessible spaces for law enforcement purposes is displayed, the latter being demonstrated to be not as strict as it seems at first glance due to its limited scope and broad exemptions. As the majority of FRTs fall within the category of high-risk AI systems, the AI Act subjects them to technological requirements, a fundamental rights impact assessment prior to their first application and provides remedies for protection of individuals such as the right to obtain an explanation on a decision taken by the AI system. The AI Act is proven to be a substantive framework for the regulation of AI and thus, despite omitting an outright ban of FRT use in publicly accessible spaces, it will probably show its full potential in the years after its entry into force.