Biological invasions by non-indigenous species (NIS) are widely recognized as a significant component of human-caused global environmental change. However, the standard programme of mapping distributions, predicting future ranges, modelling species spread, assessing impacts, developing management guidelines and screening species suffers from a number of serious limitations. NIS distribution maps can often be as misleading as they are instructive. Perceptions of the intensity, scale and rate of invasion are a function of mapping resolution, and the lack of common mapping standards prevents accurate comparative assessments. Coarse resolution data may overestimate the role of climate in the invasion process relative to other variables such as land use or human population density. Climate envelopes have therefore been widely used to predict species future ranges, but often overestimate potential distributions. Without an appropriate mechanistic understanding of the invasion process, correlative approaches may misinterpret the relative risks posed by different NIS. In addition, statistical models of invasion fail to encapsulate the complexity of human-mediated dispersal, which includes such diverse processes as transatlantic timber trade, horticultural fashion and the continuing expansion of road networks. Screening tools based on species traits, taxonomy and/or invasion history can sometimes result in high discrimination rates. Yet where the cost of false positives outweighs the risks from false negatives, a higher discriminatory power is required. Certain research outputs have perhaps been counterproductive in the war against invasive species. Studies have highlighted that only a tiny proportion of NIS are invasive, that most invasions occur in human dominated rather than pristine ecosystems, that indigenous and non-indigenous species are sufficiently similar that their impacts may not necessarily be different, and that there is evidence that introduced species augment rather than reduce species diversity. It is crucial to address these wider perceptions of the problem in order to mobilize the resources necessary for a global invasive species management programme.