Non-indigenous animal species threaten biodiversity and ecosystem stability by damaging or transforming habitats, killing or out-competing native species and spreading disease. We use World Heritage Area Kakadu National Park, northern Australia, as a focal region to illustrate the current and potential threats posed by non-indigenous animal species to internationally and nationally recognised natural and cultural values. Available evidence suggests that large feral herbivores such as Asian swamp buffalo, pigs and horses are the most ecologically threatening species in this region. This may reflect the inherent research bias, because these species are highly visible and impact primary production; consequently, their control has attracted the strongest research and management efforts. Burgeoning threats, such as the already established cane toad and crazy ant, and potentially non-indigenous freshwater fish, marine invertebrates and pathogens, may cause severe problems for native biodiversity. To counter these threats, management agencies must apply an ongoing, planned and practical approach using scientifically based and well funded control measures; however, many stakeholders require direct evidence of the damage caused by non-indigenous species before agreeing to implement control. To demonstrate the increasing priority of non-indigenous species research in Australia and to quantify taxonomic and habitat biases in research focus, we compiled an extensive biography of peer-reviewed articles published between 1950 and 2005. Approximately 1000 scientific papers have been published on the impact and control of exotic animals in Australia, with a strong bias towards terrestrial systems and mammals. Despite the sheer quantity of research on non-indigenous species and their effects, management responses remain largely ad hoc and poorly evaluated, especially in northern Australia and in high-value areas such as Kakadu National Park. We argue that improved management in relatively isolated and susceptible tropical regions requires (1) robust quantification of density–damage relationships, and (2) the delivery of research findings that stimulate land managers to develop cost-effective control and monitoring programs.