The trade of non-native pets, especially of non-domesticated and exotic animals, and their subsequent release and establishment of populations is one of the major pathways of introduction for invasive alien reptiles, amphibia, birds and mammals. Here, we use a group of arboreal mammals, tree squirrels of the genus Callosciurus, as a well-documented case study, reviewing the pathways of introduction, the current areas of non-native distribution, the rate of establishment success and the challenge and legal importance of species identification. We further illustrate the importance of early detection and effective monitoring methods and plans. Next, we document how they interfere with native species, their risk of acting as vectors for emerging infectious diseases and their potential role in maintaining parasitic infections that can affect human health. We conclude by reviewing the current management, or the lack of it, and highlight the diverse biological, social, political and economic reasons that make control/eradication of these charismatic species difficult or even impractical in most countries. However, reviewing the only two successful eradications of the IAS, we highlight the need to acknowledge the public opinion and the importance of communication, transparency and the engagement of a diversity of stakeholders to create a consensus about the actions to undertake.