<p>Artificial intelligence (AI) increasingly performs tasks once reserved for humans, raising questions about when, why and how people trust machines — and whether they should do so in the first place. In this Review, we identify six principles that help to structure an understanding of trust in AI and highlight its socially embedded nature: that trust in AI is inferred; that trustworthiness, trust and trusting behaviour are distinct; that trust in AI is about both morality and performance; and that trust in AI is agent-specific; individually variable; and strategically motivated. The inferred, multidimensional, dynamic and contextual nature of trust in AI illustrates that ‘trust in AI’ is not one thing, but varies across different systems, individuals and contexts. We end by considering broader ethical implications of studying trust in AI and argue that trust in AI requires both studying how people think and reflecting on the kind of world that trust in AI serves to create.</p>