In the Anthropocene, species are faced with drastic challenges due to rapid, human-induced changes, such as habitat destruction, pollution and biological invasions. In the case of invasions, native species may change their behaviour to minimize the impacts they sustain from invasive species, and invaders may also adapt to the conditions in their new environment in order to survive and establish self-sustaining populations. We aimed at giving an overview of which changes in behaviour are studied in invasions, and what is known about the types of behaviour that change, the underlying mechanisms and the speed of behavioural changes. Based on a review of the literature, we identified 191 studies and 360 records (some studies reported multiple records) documenting behavioural changes caused by biological invasions in native (236 records from 148 species) or invasive (124 records from 50 species) animal species. This global dataset, which we make openly available, is not restricted to particular taxonomic groups. We found a mild taxonomic bias in the literature towards mammals, birds and insects. In line with the enemy release hypothesis, native species changed their anti-predator behaviour more frequently than invasive species. Rates of behavioural change were evenly distributed across taxa, but not across the types of behaviour. Our findings may help to better understand the role of behaviour in biological invasions as well as temporal changes in both population densities and traits of invasive species, and of native species affected by them.