Approximately one-half of the major arthropod pests in the United States originated abroad. Furthermore many additional dangerous pests exist overseas. Rationales for eradicating selected introduced arthropod pests are summarized. The definition of eradication advanced by L. D. Newsom is espoused, i.e., the destruction of every individual of a species from an area surrounded by naturally occurring or man-made barriers sufficiently effective to prevent reinvasion of the area except through the intervention of man." Eradication is an important strategy for meeting certain pest problems, along with the strategies of prevention, management of local populations, and total population management. Apparently Charles Henry Fernald, University of Massachusetts, Amherst, was the first American entomologist to develop a strategy of eradication. Brief accounts are given of eradication campaigns against the gypsy moth, San Jose scale, cattle fever ticks, screwworm, khapra beetle, imported fire ants, tropical fruit flies, and boll weevil. Eradication efforts against 42 species or groups of species are summarized in a table. The strategy of eradication succeeded against 23 species, failed totally against 9 species, and was successful in some parts of the continental United States but failed in others against the remaining 10 species. Factors that influence the ease of eradication are listed. Early detection of incipient infestations of dangerous alien pests is extremely important. Most eradication campaigns have features that tend to induce emotions of outrage. Leaders of eradication campaigns need to anticipate negative reactions by the public and to be proactive in removing or mitigating those aspects that trouble the public.