New or re-emerging pathogens for humans have emerged outside of their usual endemic range during the last decade originating severe public health concern and economical losses. Climate changes have played a significant role in the emergence or re-emergence of arboviruses. Among these pathogens, several viruses belong to the Bunyaviridae family. This family is composed of RNA viruses grouped into five genera Orthobunyavirus, Hantavirus, Nairovirus, Phlebovirus and Tospovirus characterized by their antigenic, genetic and ecological properties. These viruses use cellular proteins to promote their own replication/transcription and reciprocally the host induces, in response, an important transcriptional reprogramming to activate antiviral defences including the interferon type I pathways. The virulence of the pathogenic bunyaviruses is directly linked to the roles of viral virulence factors and their capacity to counteract the host pathways. This review summarizes the various strategies developed by the different genera of the Bunyaviridae family to overcome and escape the innate immune response and eventually other cellular functions.