Based on a comprehensive review of literature and OIE (World Animal Health Organisation) outbreak reports, this scientific opinion reports, first, that there is no evidence that Rift Valley fever (RVF) has spread to previously uninfected countries during the past 10 years. Nevertheless, RVF has moved north within Mauritania, in a desert area. Secondly, maps of Europe and the southern Mediterranean Basin are provided, displaying the geographic distribution of the reported presence of nine potentially competent Rift Valley fever virus (RVFV) vectors of the region, based on a systematic literature review. From environmental and eco-climatic data, predicted presence maps were generated that suggest the suitability of several parts of Europe and the southern Mediterranean Basin for these potentially competent RVFV vectors. Thirdly, to assess the risk of introduction of RVFV into some designated countries in the southern Mediterranean Basin (hereafter defined as the region concerned, RC), especially through the movements of live animals and vectors, a quantitative model was constructed and model parameters were derived based on expert knowledge elicitation (EKE). The EKE model indicates that some hundreds of RVFV-infected animals will be moved into the RC when an epidemic in the source areas occurs. The risk of RVFV entering the RC through the movement of vectors is expected to be small in comparison with the risk of entry through infected animals. Because of a lack of quantitative information on the seasonality of vector abundance and vertical transmission of RVFV within local vector species, the risk of endemicity could not be assessed. However, based on the abundance of the vector Culex pipiens, the livestock densities and the temperature in the region, there is a potential for the occurrence of RVF spread in the coastal areas of the RC.