International audienceThis paper focuses on similarity caching systems, in which a user request for an object o that is not in the cache can be (partially) satisfied by a similar stored object o', at the cost of a loss of user utility. Similarity caching systems can be effectively employed in several application areas, like multimedia retrieval, recommender systems, genome study, and machine learning training/serving. However, despite their relevance, the behavior of such systems is far from being well understood. In this paper, we provide a first comprehensive analysis of similarity caching in the offline, adversarial, and stochastic settings. We show that similarity caching raises significant new challenges, for which we propose the first...