The chapter explores the relationship between artificial intelligence and public administrations. It is structured into three parts. The first part examines the different types of artificial intelligence and the various ways in which public administration can employ it, in order to assess the risks and highlight the opportunities it presents. The second part analyzes the framework of national and European regulations governing the use of AI in the exercise of public functions, with particular attention to the case law of national courts and the complex European regulatory framework, represented by Regulation 2024/1689 (AI Act). The third part focuses on the main challenges facing algorithmic administration, including the adequate training of public officials, the procurement processes necessary to equip the administration with AI systems, and the role of cybersecurity, whose importance grows as public administration accelerates its digitalization process.