Over the past decades, various free-living animals (hosts) and their parasites have invaded recipient areas in which they had not previously occurred, thus gaining the status of aliens or exotics. In general this happened to a low extent for hundreds of years. With variable frequency, invasions have been followed by the dispersal and establishment of non-indigenous species, whether host or parasite. In the literature thus far, colonizations by both hosts and parasites have not been treated and reviewed together, although both are usually interwoven in various ways. As to those factors permitting invasive success and colonization strength, various hypotheses have been put forward depending on the scientific background of respective authors and on the conspicuousness of certain invasions. Researchers who have tried to analyse characteristic developmental patterns, the speed of dispersal or the degree of genetic divergence in populations of alien species have come to different conclusions. Among parasitologists, the applied aspects of parasite invasions, such as the negative effects on economically important hosts, have long been at the centre of interest. In this contribution, invasions by hosts as well as parasites are considered comparatively, revealing many similarities and a few differences. Two helminths, the liver fluke, Fasciola hepatica, of cattle and sheep and the swimbladder nematode, Anguillicola crassus, of eels are shown to be useful as model parasites for the study of animal invasions and environmental global change. Introductions of F. hepatica have been associated with imports of cattle or other grazing animals. In various target areas, susceptible lymnaeid snails serving as intermediate hosts were either naturally present and/or were introduced from the donor continent of the parasite (Europe) and/or from other regions which were not within the original range of the parasite, partly reflecting progressive stages of a global biota change. In several introduced areas, F. hepatica co-occurs with native or exotic populations of the congeneric F. gigantica, with thus far unknown implications. Over the fluke's extended range, in addition to domestic stock animals, wild native or naturalized mammals can also serve as final hosts. Indigenous and displaced populations of F. hepatica, however, have not yet been studied comparatively from an evolutionary perspective. A. crassus, from the Far East, has invaded three continents, without the previous naturalization of its natural host Anguilla japonica, by switching to the respective indigenous eel species. Local entomostrac crustaceans serve as susceptible intermediate hosts. The novel final hosts turned out to be naive in respect to the introduced nematode with far reaching consequences for the parasite's morphology (size), abundance and pathogenicity. Comparative infection experiments with Japanese and European eels yielded many differences in the hosts' immune defence, mirroring coevolution versus an abrupt host switch associated with the introduction of the helminth. In other associations of native hosts and invasive parasites, the elevated pathogenicity of the parasite seems to result from other deficiencies such as a lack of anti-parasitic behaviour of the naïve host compared to the donor host which displays distinct behavioural patterns, keeping the abundance of the parasite low. From the small amount of available literature, it can be concluded that the adaptation of certain populations of the novel host to the alien parasite takes several decades to a century or more. Summarizing all we know about hosts and parasites as aliens, tentative patterns and principles can be figured out, but individual case studies teach us that generalizations should be avoided.