Artificial intelligence (AI) has the potential to radically transform our society. It may lead to a massive increase in the capabilities of humankind and allow us to address some of our most intractable challenges. It may also entail profound disruption to structures and processes that have sustained our society over centuries. These developments present a unique challenge to the socio-economic constitutional arrangements which govern our world at national, regional and international level. The deployment of increasingly powerful AI systems, able to function with increasing degree of autonomy, has led to concerns over loss of human control of important societal processes, over the disruption of existing economic, social and legal relationships, and over the empowerment of some societal actors at the expense of others, together with the entrenchment of situations of domination or discrimination. It has also made increasingly clear how tremendous the potential benefits, that these technologies may bring, are to those who successfully develop and deploy them. There is therefore great pressure on governments, international institutions, public authorities, civil society organisations, industry bodies and individual firms to introduce or adapt mechanisms and structures that will avoid the potentially negative outcomes of AI and achieve the positive ones. These mechanisms and structures, which have been given the umbrella term 'AI governance', cover a wide range of approaches, from individual firms introducing ethical principles which they volunteer to abide by, to the European Union legislating an AI Act, which will prohibit certain types of AI applications and impose binding obligations on AI developers and deployers. The fast pace of innovation in the development of AI technologies is mirrored by the fast pace of development of the emerging field of AI governance, where traditional legislation by public bodies is complemented with more innovative approaches, such ashybrid and adaptive governance, ethical alignment, governance by design and the creation of regulatory sandboxes. The chapter "AI and Sensitive Personal Data Under the Law Enforcement Directive: Between Operational Efficiency and Legal Necessity" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.