A key conundrum is how cells adapt to rapidly activate innate immune pathways upon sensing viruses, while limiting their activation under homeostasis. The formation of biomolecular condensates such as stress granules (SGs) allows the cell to tightly regulate RNA metabolism and cellular signalling in response to stress, including viral RNAs. During infection in mammalian cells, different SGs or SG-like foci can assemble and are proposed to regulate antiviral signalling pathways. Some viruses also hijack phase separation to promote replication and thus condensates can play antiviral roles or promote replication. How and why these condensates play different roles is unknown and the subject of debate. Our aim is to advance the understanding of SG biology and its interface with viral infections using important pathogens of animals or humans. Our results demonstrate that mosquito-transmitted yellow fever virus (YFV) induces assembly of unique SGs. Combining compositional and functional studies, we show that they sequester proteins associated with antiviral and mitochondrial functions associated and that infection impairs mitochondrial homeostasis. In contrast, using animal cell models, infection with the livestock pathogen foot-and-mouth disease virus induce the formation of SGs uncoupled from innate immune signalling but associated with cell survival to promote replication; while the key chicken pathogen infectious bronchitis virus induces SGs that activate antiviral responses. This reflects a complex interplay between viral sensing, condensates assembly and the regulation of key cellular functions, that are fine-tuned in a virus and cell – specific manner, and define novel infection biology rules.