Two examples of the introduction of non-indigenous invasive species are reviewed: the grey squirrel in Europe (United Kingdom, Ireland and Italy) and the brushtail possum in New Zealand. Both have become very successful in their respective non-native habitats since their introductions in the mid-to-late 19th Century. Both species impact extensively on native biodiversity, environmental sustainability, forestry, and agriculture through a range of direct and indirect mechanisms. Management is currently mainly by lethal control, namely poisoning, trapping and shooting. Such methods of control are, however, increasingly contentious for both species, and alternative, non-lethal methods of population control, e.g. fertility control, are being developed. The case studies highlight many of the issues in invasive animal control; for example, prevention being better than control, lack of good understanding of impacts and the success of control measures on reducing impacts, interactive impacts on native biodiversity and ecosystems, the telling influence of public opinion on management options and, lastly, the need to better inform and educate the public.