Abstract Biological invasions are a major driver of biodiversity loss, but no study has described the scope of threats to bats (Chiroptera) by invasive species. We reviewed the literature for negative effects of invasive species to bats and summarised threats according to four categories: predation, disease, competition, and indirect interactions. We identified threats of 37 invasive species to 40 bat species. Ten bat species were threatened by more than one invasion pathway. About 38 percent of cases are speculative and 18 percent circumstantial, many attributed to overlapping ranges, and most accounts do not quantify effects needed to forecast bat population impacts. Evidence of cat predation is frequently cited, constituting the greatest incidence of observational data. Other direct and indirect impacts were documented from goats, dogs, brown tree snake, rainbow lorikeet, rose‐ringed parakeet, yellow crazy ant, giant centipede, palm, burdock, avian cholera, and white‐nose syndrome. Circumstantial evidence suggests impacts by rats, stoats, coqui frog, common wolf snake, little fire ant, kudzu, and Lantana camara. Other impacts by giant centipede, yellow crazy ant, cats, goats, rats, and avian cholera are speculative, as are those from pigs, deer, white eye, common starling, house sparrow, rock dove, barn and little owls, brush‐tailed possum, honeybee, wasp, phytophagous insects, tamarisk, Cinnamomum verum, and Tabebuia pallida. Over 60 percent of bat species reviewed are island‐dwelling, corresponding with evidence indicating that most extinctions occur on islands and invasive species’ impacts are worse for island than mainland populations. Although appreciable bat population reductions owing to invasive species are often unproven, invasions are likely to exacerbate effects of other vulnerabilities. Multiple invaders and synergistic interactions may ultimately lead to species losses. Managers should exercise the precautionary principle by taking action against non‐native species when first detected, even if new species do not appear to be detrimental.