Artificial intelligence (AI) is changing the world we live in, and it has the potential to transform struggling healthcare systems with new efficiencies, new therapies, new diagnostics, and new economies. Already, AI is having an impact on healthcare, and new prospects of far greater advances open up daily. This paper sets out how AI can bring new precision to care, with benefits for patients and for society as a whole. But it also sets out the conditions for realizing the potential: key issues are ensuring adequate access to data, an appropriate regulatory environment, action to sustain innovation in research institutes and industry big and small, promotion of take-up of innovation by the healthcare establishment, and resolution of a range of vital legal and ethical questions centred on safeguarding patients and their rights. For Europe to fulfil the conditions for success, it will have to find a new spirit of cooperation that can overcome the handicaps of the continent's fragmented technical and legal landscape. The start the European Union has made shows some ambition, but a clearer strategic vision and firmer plans for implementation will be needed. The European Alliance for Personalised Medicine (EAPM) has listed its own priorities: data, integrating innovation into care, building trust, developing skills and constructing policy frameworks that guarantee infrastructure, equitable access, and legal clarity.