Because of the damage some do, including threatening biodiversity, invasive species are a current focus of interest, particularly outside Europe. Yet invasion biology is still struggling to become analytic. Progress has been made in quantifying the proportion of invaders that succeed in various ways, and in measuring the degree of that success. Several examples, where the course of invasion has been explained, show the variation in biological processes involved. A detailed analysis, often with experiments and modelling, is necessary for a satisfactory explanation. Prediction is harder than explanation. Attempts at predicting invasions have generally been unsatisfactory. Ten reasons that may contribute to this are discussed. Progress will require defining more precisely what is to be predicted and measuring more quantitatively the ecological properties of species. Even so, predicting the ecological behaviour of a species in a new environment may be effectively impossible.