Abstract. Of the extant species of land mammals, 124 (2.6%) can be classed as 'successful invaders', whereas 1038 (21.6%) are classed as threatened, according to the 2006 IUCN Red List. Relatively high proportions of successful invaders are found among Artiodactyla, Carnivora, Lagomorpha and Perissodactyla. Compared with other organisms, mammals seem relatively likely to become established when introduced outside their natural range. Studies of determinants of invasion success indicate that the number of individuals released, the size of the natural range of the introduced species, and the temperateness of climate in the new range can all increase the probability of establishment of introduced mammals. Negative impacts of invasive mammals on native biodiversity include direct effects such as predation, browsing and competition, but can extend to disruption of patterns of nutrient flow, and trophic cascades. Eradication of several species of invasive mammals from increasingly large areas is now possible. In this context, it is important to better understand ecological interactions between such mammals (and between them and other species) to avoid unwanted consequences such as mesopredator or competitor release, after the removal of particular species. Finally, it is increasingly apparent that research is needed on the behaviour of dispersing and invading individuals, to improve the early detection of new mammal invasions or reinvasions.