Insects have for millennia presented human society with some of its greatest development challenges by spreading diseases, consuming crops and damaging infrastructure. Despite the massive human and financial toll of invasive insects, cost estimates of their impacts remain sporadic, spatially incomplete and of questionable quality. We compiled the most comprehensive database of economic costs of invasive insects, expressing historical estimates in annual 2014-equivalent US dollars. Taking all reported goods and services estimates, invasive insects cost a minimum of US$70.0 billion year-1 globally, while global health costs directly attributable to invasive insects exceed US$6.9 billion year-1. Total costs rise as the number of estimates increases, although many of the worst costs have already been estimated (especially those related to human health). A lack of dedicated studies, especially for reproducible goods and services estimates, implies gross underestimation of global costs. Global warming as a consequence of climate change, rising human population densities and intensifying international trade will allow the costliest insects to spread into new areas, although substantial savings could be achieved by increasing surveillance, containment and public awareness.