Biological invasions are characterized by remarkable spatio-temporal dynamics, with many species having extended their distribution range from within a single region to much of the globe within the last century. The comparative analysis of the spatio-temporal dynamics of over 100 taxa from studies undertaken worldwide provides the basis of a critical assessment of current knowledge. At the scale of single habitats, simple reaction-diffusion models may be accurate enough to predict the spread of new invaders without recourse to complex life history parameterization. Average rates of local spread reported for invasive species in the literature range from 2 m · y⁻¹ to a maximum of 370 m · y⁻¹. Average rates of long-distance dispersal are at least two orders of magnitude greater than estimates of local dispersal, with a maximum of 167 km · y⁻¹. While local-scale studies do pick up dispersal events of several kilometres, study sites are rarely sufficiently large or monitored for long enough to characterize these events accurately. Long-distance dispersal events may occur during periods of negligible population increase and appear to bear little relationship to population size. At regional scales, invasive species rarely move across the landscape as a continuous front and both local and long-distance dispersal determine spatial patterns. At these larger spatial scales, both local and long-distance dispersal require parameterization, and this has been achieved through spatially explicit individual-based simulation models using two or more dispersal functions. It is doubtful whether a single estimate of spread encapsulates the spatio-temporal dynamics of invasive species at this scale. Thus, estimates of spread drawn from successive distribution maps will tend to be biased towards long-distance dispersal events. The frequency and distribution of introduction events play a key role in invasion trajectories, and the stochastic nature of such events may explain why the longer a species has been introduced into a region the greater the likelihood that it becomes invasive. However, cumulative counts of localities or samples only provide one perspective on the invasion process and need to be associated with spatial information to depict spread more realistically. This review highlights that monitoring of invasive species must be approached from a hierarchical perspective with data gathered at more than one spatial scale. Such an approach will improve predictions and integrate landscape attributes into invasion dynamics.