Invasive species are a global phenomenon and the rate of biological invasion is only increasing as human trade and transport, together with climate change, cause the rapid reorganisation of species distributions. The impacts of invasive species can be both severe and wide ranging, adversely affecting native ecosystems, human health, agriculture, and economies. Therefore, understanding how species become invasive and subsequently inflict damage on host environments is imperative. Additionally, once an incursion has occurred, its rapid detection and ongoing monitoring are essential for management measures to be effective. My thesis aimed to further a greater understanding of behavioural evolution in invasive species and advance the application of genetic tools to inform and enhance the prediction, monitoring, and management of invasion events. In the first analysis (Chapter 2), I reviewed the scientific literature reporting behavioural changes in the traits of invasive species when compared to the mean traits of conspecifics in the native range. In this research, I demonstrated that, while behavioural changes are widely reported across invasive taxa, our understanding of the possible mechanisms enabling these changes – plasticity and adaptive evolution – are poorly understood. In addition, research on the fundamental molecular and genetic processes that underlie measured phenotypic changes is in its infancy. Moving forward, I recommend that opportunities to study new or recent biological invasions should be rapidly exploited such that temporal studies can be used to identify patterns of change that occur during invasion. In Chapter 3, I investigated the application of environmental DNA (eDNA: genetic material released by organisms into the environment) – an increasingly popular biomonitoring method that has yet to be optimised for lacustrine environments – to the detection and monitoring of the invasive brown bullhead catfish (Ameiurus nebulosus). I sampled lakes across two regions of the North Island of New Zealand and compared the results from different field (filter pore sizes, fyke nets) and laboratory (eDNA assays) protocols. I found that species-specific assays (quantitative PCR and catfish-specific metabarcoding) had the highest rates of catfish detection and further showed that multi-species metabarcoding assays were correlated with catfish capture from fyke nets. This indicates that species-specific assays may be the most effective where detection is the primary goal, while multi-species assays hold some promise for producing semi-quantitative results. Therefore, I recommend the development of standardised, flexible, eDNA protocols that will ensure their sound application and interpretation. As species continue to move beyond their natural ranges, the need for a better mechanistic understanding of invasion, and for more effective detection and monitoring methods, is increasing. With technological advances and increasing availability of genomic data, more rapidly identifying new incursions and studying invasions in real time will lead to better understanding, monitoring, and management of invasive species.