Rift Valley fever (RVF), a vector-borne zoonotic disease caused by a phlebovirus (family Bunyaviridae), is considered to be one of the most important viral zoonoses in Africa. It is also a potential bioterrorism agent. Transmitted by mosquitoes or by direct contact with viraemic products, RVF affects both livestock and humans, causing abortion storms in pregnant ruminants and sudden death in newborns. The disease provokes flu syndrome in most human cases, but also severe encephalitic or haemorrhagic forms and death. There is neither a treatment nor a vaccine for humans. The disease, historically confined to the African continent, recently spread to the Arabian Peninsula and Indian Ocean. Animal movements, legal or illegal, strongly contribute to viral spread, threatening the Mediterranean basin and Europe, where competent vectors are present. Given the unpredictability of virus introduction and uncertainties about RVF epidemiology, there is an urgent need to fill the scientific gaps by developing large regional research programmes, to build predictive models, and to implement early warning systems and surveillance designs adapted to northern African and European countries.