Unlike many segmented negative-sense RNA viruses, most members of the Bunyavirales bud at Golgi membranes, as opposed to the plasma membrane. Central players in this assembly process are the envelope glycoproteins, Gn and Gc, which upon translation undergo proteolytic processing, glycosylation and trafficking to the Golgi, where they interact with ribonucleoprotein genome segments and bud into Golgi-derived compartments. The processes involved in genome packaging during virion assembly can lead to the generation of reassorted viruses, if a cell is co-infected with two different bunyaviruses, due to mismatching of viral genome segment packaging. This can lead to viruses with high pathogenic potential, as demonstrated by the emergence of Schmallenberg virus. This review focuses on the assembly pathways of tri-segmented bunyaviruses, highlighting some areas in need of further research to understand these important pathogens with zoonotic potential.