We developed the DAMA (Distribution of Alien MAmmals) database, a comprehensive source reporting the global distribution of the 230 species of mammals that have established, self‐sustaining and free‐ranging populations outside their native range due to direct or indirect human action. Every alien range is accompanied by information on its invasion stage, pathway, method of introduction and date of introduction. We collected information from 827 different sources (scientific literature, books, risk assessments, reports, online biodiversity databases and websites), and used it to draw alien range maps for these species following the IUCN mapping framework. DAMA comprises 2726 range polygons, covering 199 Countries, 2190 level 1 administrative areas and 11 zoogeographic realms for the period 21500 BC‐AD 2017. The most represented orders among introduced mammal species are Rodentia (n=58, 25.22%), Cetartiodactyla (n=49 species, 21.30%), Carnivora (n=30 species, 13.04%), Diprotodontia (n=28, 12.17%) and Primates (n=26, 11.30%). Mammal species have been frequently introduced for hunting (n=100), pet trade (n=57), conservation (n=51) and fauna improvement (n=42). The majority of range polygons are placed on islands (n=2196, 80.56%), encompass populations that have moved beyond establishment and into the invasion stage (n=1655, 60.71%), and originated from 1500 AD to the present (n=1496, 54.88%). Despite inheriting literature biases towards more studied regions (e.g., developed Countries), DAMA is the most up‐to‐date picture of alien mammal global distribution and can be used to investigate their invasion ecology across different biogeographical regions. There are no copyright or proprietary restrictions; IUCN range maps were modified into a derivative work according to the IUCN’s terms of service.