We use the term ‘aggressive mimic’ for predators that communicate with their prey by making signals to indirectly manipulate prey behaviour. For understanding why the aggressive mimic's signals work, it is important to appreciate that these signals interface with the prey's perceptual system, and that the aggressive mimic can be envisaged as playing mind games with its prey. Examples of aggressive mimicry vary from instances in which specifying a model is straight forward to instances where a concise characterization of the model is difficult. However, the less straightforward examples of aggressive mimicry may be the more interesting examples in the context of animal cognition. In particular, there are spiders that prey on other spiders by entering their prey's web and making signals. Web invasion brings about especially intimate contact with their prey's perceptual system because the prey spider's web is an important component of the prey spider's sensory apparatus. For the web-invading spider, often there is also a large element of risk when practising aggressive mimicry because the intended prey is also a potential predator. This element of risk, combined with exceptionally intimate interfacing with prey perceptual systems, may have favoured the web-invading aggressive mimic's strategy becoming strikingly cognitive in character. Yet a high level of flexibility may be widespread among aggressive mimics in general and, on the whole, we propose that research on aggressive mimicry holds exceptional potential for advancing our understanding of animal cognition.