The SCOPE programme on the ecology of biological invasions addresses three questions: What are the factors that determine whether a species will become an invader or not? What are the site properties which determine whether an ecological system will be relatively prone to or resistant to invasion? How should management systems be developed to best advantage, given the knowledge gained by attempting to answer the first two questions? The answers that have been offered to these questions earlier, and during the course of the programme, are reviewed. The consensus is that, although certain habitat and biological features increase the probability of invasion and establishment, these features are neither necessary nor sufficient, and that the prediction of invasion is not yet feasible. These points are illustrated by examples and generalizations from a survey of British invaders. The probability that an established invader will be a pest in Britain seems to be around 10%. Mathematical modelling may help in understanding and, later, in predicting invasions. Models indicate that establishment may be more critical than spread, and that a successful invader will spread at a constant linear speed. Models and data suggest that both an accelerating rate of spread and occasional major jumps can be expected; consequently, efforts to eliminate an invader at an early stage will be the most effective.