Aim: Although global trade is implicated in biological invasions, the assumption that trade networks explain the large-scale distributions of non-native species remains largely untested. We addressed this by analysing relationships between global trade networks and plant pest invasion. Location: Forty-eight countries in Europe and the Mediterranean. Time period: Current. Major taxa studied: Four hundred and twenty-two non-native plant pests (173 invertebrates, 166 pathogens, 83 plants). Methods: Ten types of connectivity index were developed, representing potential roles of trade networks, air transport links, geographical proximity, climatic similarity and source country wealth in facilitating invasion. Generalized linear mixed models (GLMMs) identified the connectivity index that best explained both historical and recent invasion. Then, more complex GLMMs were developed including connectivity through trade networks for multiple commodities relevant for pests (live plants, forest products, fruit and vegetables and seeds) and species' transport associations with those commodities. Results: Total import volumes, species' global prevalence and connectivity measures based on air transport, geographical distance or climate did not explain invasion as well as connectivity through global trade networks. Invasion was strongly promoted by agricultural imports from countries in which the focal species was present and that were climatically similar to the importing country. However, live plant imports from nearby countries provided a better explanation of the most recent invasions. Connectivity through multiple trade networks predicted invasion better than total agricultural trade, and there was support for our hypothesis that species known to be transported with a particular network had greater sensitivity to its connectivity. Main conclusions: Our findings show that patterns of invasion are governed to a large extent by global trade networks connecting source areas for non-native species and the dispersal of those species through multiple trade networks. This enhances potential for developing a predictive framework to improve risk assessment, biosecurity and surveillance for invasions.