The spread of invasive species continues to provide significant challenges to researchers and those government biosecurity agencies charged with protecting a country’s borders. In an increasingly connected world, these invasive species are potentially able to spread further and more rapidly. Transport networks such as the global shipping network or tourist movement networks represent just two examples of networks that can facilitate the human mediated spread of invasive species. I will discuss some of the work I am or have been involved in, which examines and models transport networks. Examples of this work includes modelling the spread of invasive species via shipping containers, development of a real time tool for analysing ships arriving into Australia for their risk of carrying Asian gypsy moth eggs, informal trade networks in SE Asia, and tourist movement networks in New Zealand, as well as a global analysis of the threat from crop pests and pathogens.