Invasive populations cause adverse impacts on ecosystems, agriculture, and economic activities. Advancing understanding of how populations respond to environmental changes and develop their invasive status will enable improved prediction, prevention, and management of ecological invasions. Here, we review recent literature and find that behavioural shifts within species across native and invasive populations are common during invasion. We collate examples which demonstrate how behaviours associated with invasion can be an outcome of plastic, pre-adaptive, and/or post-adaptive processes. However, we find that research investigating the molecular basis of observed behavioural shifts associated with invasion is limited. Important research (but perhaps the most challenging to conduct), is the long-term study of ongoing invasions that track species’ behaviour and genetic change throughout the stages of the invasion process. Additionally, future research should aim to establish whether behavioural shifts originate from plasticity, microevolutionary processes, or a combination of both. Common garden experiments (using distinct populations grown under shared conditions), carried out in conjunction with genetic studies that track changes at the molecular level, could aid this endeavour.