The invasion of alien species into areas beyond their native ranges is having profound effects on ecosystems around the world. In particular, novel alien predators are causing rapid extinctions or declines in many native prey species, and these impacts are generally attributed to ecological naïveté or the failure to recognise a novel enemy and respond appropriately due to a lack of experience. Despite a large body of research concerning the recognition of alien predation risk by native prey, the literature lacks an extensive review of naïveté theory that specifically asks how naïveté between novel pairings of alien predators and native prey disrupts our classical understanding of predator-prey ecological theory. Here we critically review both classic and current theory relating to predator-prey interactions between both predators and prey with shared evolutionary histories, and those that are ecologically 'mismatched' through the outcomes of biological invasions. The review is structured around the multiple levels of naïveté framework of Banks & Dickman (2007), and concepts and examples are discussed as they relate to each stage in the process from failure to recognise a novel predator (Level 1 naïveté), through to appropriate (Level 2) and effective (Level 3) antipredator responses. We discuss the relative contributions of recognition, cue types and the implied risk of cues used by novel alien and familiar native predators, to the probability that prey will recognise a novel predator. We then cover the antipredator response types available to prey and the factors that predict whether these responses will be appropriate or effective against novel alien and familiar native predators. In general, the level of naïveté of native prey can be predicted by the degree of novelty (in terms of appearance, behaviour or habitat use) of the alien predator compared to native predators with which prey are experienced. Appearance in this sense includes cue types, spatial distribution and implied risk of cues, whilst behaviour and habitat use include hunting modes and the habitat domain of the predator. Finally, we discuss whether the antipredator response can occur without recognition per se, for example in the case of morphological defences, and then consider a potential extension of the multiple levels of naïveté framework. The review concludes with recommendations for the design and execution of naïveté experiments incorporating the key concepts and issues covered here. This review aims to critique and combine classic ideas about predator-prey interactions with current naïveté theory, to further develop the multiple levels of naïveté framework, and to suggest the most fruitful avenues for future research.