The yellow-legged hornet (Vespa velutina) is the first invasive Vespidae predator of honeybees to be accidentally introduced into Europe from Asia. In the current pollinator decline, V. velutina is an additional stressor for honeybees and other pollinators. Although V. velutina contributes to the loss of honeybee colonies, little is known about its biology and behaviour both in the native and in the invaded area. Here, we review the current knowledge of this species and describe its life cycle and life history traits (reproduction, overwintering, foraging and dispersal) in the light of the biology of other Vespidae. We also review the impact of this species on ecosystems, on the economics of beekeeping, and on human health (this species being potentially deadly for allergic people). Based on this information and on previous worldwide experiences with Vespidae invasions, we propose key research topics for the development of effective management plans. We identify methods to limit the impact and proliferation of V. velutina in Europe that are based on nest destruction, trapping, population genetics, and biological control. In our opinion, research effort on the means to detect and destroy V. velutina nests at an early stage is required in order to short-circuit the colony cycle and thus limit both its impact on honeybees and its expansion through Europe. Finally, we discuss the impact of this biological invasion on the development of methods that should be used to manage alien species in the future.