The impact of invasive species on native vegetation is a major threat to biodiversity all over the world - a threat ranked second only to habitat destruction. Other negative effects of weed invasions include reduced ecosystem services, loss to agricultural production and impacts on human health. This work covers the discipline of risk assessment as applied to the invasion ecology of plants. Taking a global context, it synthesizes theories on plant invasions, introduces a variety of models for weed risk assessment, and addresses procedures for ranking invasive species on a range of scales to determine weeds of national significance. It shows how the application of risk assessment to weed invasion may help reduce weed impact and thereby improve living conditions for people throughout the world. This text is aimed at invasions ecologists, botanists, quarantine officers, policy-makers and community groups wanting to know more about this developing discipline.