The Bunyaviridae is a family of arboviruses including both plant- and vertebrate-infecting representatives. The Tospovirus genus accommodates plant-infecting bunyaviruses, which not only replicate in their plant host, but also in their insect thrips vector during persistent propagative transmission. For this reason, they are generally assumed to encounter antiviral RNA silencing in plants and insects. Here we present an overview on how tospovirus nonstructural NSs protein counteracts antiviral RNA silencing in plants and what is known so far in insects. Like tospoviruses, members of the related vertebrate-infecting bunyaviruses classified in the genera Orthobunyavirus, Hantavirus and Phlebovirus also code for a NSs protein. However, for none of them RNA silencing suppressor activity has been unambiguously demonstrated in neither vertebrate host nor arthropod vector. The second part of this review will briefly describe the role of these NSs proteins in modulation of innate immune responses in mammals and elaborate on a hypothetical scenario to explain if and how NSs proteins from vertebrate-infecting bunyaviruses affect RNA silencing. If so, why this discovery has been hampered so far.