Abstract The spread of invasive species is a threat to ecosystems worldwide. However, we know relatively little about how invasive species affect the behaviour of native animals, even though behaviour plays a vital role in the biotic interactions which are key to understanding the causes and impacts of biological invasions. Here, we explore how invasive plants – one of the most pervasive invasive taxa – impact the behaviour of native animals. To promote a mechanistic understanding of these behavioural impacts, we begin by introducing a mechanistic framework which explicitly considers the drivers and ecological consequences of behavioural change, as well as the moderating role of environmental context. We then synthesise the existing literature within this framework. We find that while some behavioural impacts of invasive plants are relatively well‐covered in the literature, others are supported by only a handful of studies and should be explored further in the future. We conclude by identifying priority topics for future research, which will benefit from an interdisciplinary approach uniting invasion ecology with the study of animal behaviour and cognition.