In this review, we relate theoretical work on the importance of surprise in cognition to empirical research relevant to surprise in predator–prey interactions. There have been multiple proposals as to how surprise should be defined and quantified in the context of animal cognition, including contributions from associative learning, information theory, Bayesian inference and the recent framework of active inference. We argue that active inference provides a novel and powerful approach to quantifying surprise and advances the field by revealing how proactive behaviour on the part of predators relates to reducing surprise. The active inference framework encompasses both proximate (e.g. neurobiological) and ultimate (evolutionary) aspects of surprise and brings new insights into key aspects of prey defences that exploit predator surprise. We focus on surprise in defences that involve a sudden change in prey appearance (such as deimatic displays), and in defences that increase prey unpredictability (such as variation in chemical defences). We review literature that have investigated these phenomena and connect them to active inference. We also consider how multiple prey defences impact surprise in predators. Finally, we consider the implications of active inference for future studies of predator–prey interactions, illustrate how this approach can be used to quantify surprise in prey defences and predict predator behaviour, and outline key questions that can be addressed within this framework. Read the free Plain Language Summary for this article on the Journal blog.