Invasive, alien plants and pollinators have varying effects on their interaction partners, ranging from highly beneficial to strongly detrimental. To understand these contrasting impacts, we review the benefits and costs associated with plant–pollinator interactions and enquire as to how the presence of abundant invaders affects the benefit–cost balance. We provide a conceptual framework that predicts that mutualism shifts to antagonism when invaders increase disproportionally in abundance relative to their interaction partners. This outcome is illustrated by an empirical example of a crop in which flower damage and an associated reduction in fruit quality represent interaction costs of intense visitation by invasive bees. More generally, the extremely high density of invasive flower visitors, such as Apis mellifera and Bombus terrestris, might have population- and community-level consequences by hampering reproduction of native plants while promoting reproduction of alien plants. Furthermore, modification of the structure of pollination networks resulting from intense visitation of native plants by superabundant alien flower visitors in highly invaded communities could predict accentuated interaction costs for many native plants. Owing to their high density and the exclusion of native pollinators, invasive bees, originally introduced for honey production and crop pollination, may negatively impact both the native biota and agriculture.