An ability to predict the rate at which an organism spreads its range is of growing importance because the process of spread (during invasion by an exotic species) is almost identical to that occurring at the expanding range margins of a native species undergoing range shifts in response to climate change. Thus, the methods used for modelling range spread can also be employed to assess the distributional implications of climate change. Here we review the history of research on the spread of cane toads in Australia and use this case study to broadly examine the benefits and pitfalls of various modelling approaches. We show that the problems of estimating the current range, predicting the future range, and predicting the spread rate are interconnected and inform each other. Generally, we argue that correlative approaches to range-prediction are unsuitable when applied to invasive species and suggest that mechanistic methods are beginning to look promising (despite being more difficult to execute), although robust comparisons of correlative versus mechanistic predictions are lacking. Looking to the future, we argue that mechanistic models of range advance (drawing from both population ecology and environmental variation) are the approaches most likely to yield robust predictions. The complexity of these approaches coupled with the steady rise in computing power means that they have only recently become computationally tractable. Thus, we suggest that the field is only recently in a position to incorporate the complexity necessary to robustly model the rate at which species shift their range.