What stories are told in national artificial intelligence (AI) policies? Combining the novel technique of structural topic modeling (STM) and qualitative narrative analysis, this paper explores and examines the policy narratives in 33 countries’ national AI policies. We uncover six common narratives that are dominating the political agenda concerning AI. Our findings show that the policy narratives’ salience vary across time and countries. The paper makes several contributions. First, our narratives describe well‐grounded, supportable conceptions of AI in governments, so as to contextualize and order a novel, multilayered, and controversial phenomenon. Building on the premise that human sensemaking is best represented and supported by narration, the paper addresses the applied rhetoric of governments to either belittle the risks or exalt the opportunities of AI. Second, we uncover the three prominent roles governments aim to take with regard to AI implementation, these are the role as enabler, leader, or regulator. Third, we make a methodological contribution toward data-driven computationally intensive theory development. Our methodological approach and identified narratives present key starting points for further research.