Predicting which species are likely to cause serious impacts in the future is crucial for targeting management efforts, but the characteristics of such species remain largely unconfirmed. We use data and expert opinion on tropical and subtropical grasses naturalised in Australia since European settlement to identify naturalised and high-impact species and subsequently to test whether high-impact species are predictable. High-impact species for the three main affected sectors (environment, pastoral and agriculture) were determined by assessing evidence against pre-defined criteria. Twenty-one of the 155 naturalised species (14%) were classified as high-impact, including four that affected more than one sector. High-impact species were more likely to have faster spread rates (regions invaded per decade) and to be semi-aquatic. Spread rate was best explained by whether species had been actively spread (as pasture), and time since naturalisation, but may not be explanatory as it was tightly correlated with range size and incidence rate. Giving more weight to minimising the chance of overlooking high-impact species, a priority for biosecurity, meant a wider range of predictors was required to identify high-impact species, and the predictive power of the models was reduced. By-sector analysis of predictors of high impact species was limited by their relative rarity, but showed sector differences, including to the universal predictors (spread rate and habitat) and life history. Furthermore, species causing high impact to agriculture have changed in the past 10 years with changes in farming practice, highlighting the importance of context in determining impact. A rationale for invasion ecology is to improve the prediction and response to future threats. Although our study identifies some universal predictors, it suggests improved prediction will require a far greater emphasis on impact rather than invasiveness, and will need to account for the individual circumstances of affected sectors and the relative rarity of high-impact species.