Cells have evolved highly specialized sentinels that detect viral infection and elicit an antiviral response. Among these, the stress-sensing protein kinase R, which is activated by double-stranded RNA, mediates suppression of the host translation machinery as a strategy to limit viral replication. Non-translating mRNAs rapidly condensate by phase separation into cytosolic stress granules, together with numerous RNA-binding proteins and components of signal transduction pathways. Growing evidence suggests that the integrated stress response, and stress granules in particular, contribute to antiviral defense. This review summarizes the current understanding of how stress and innate immune signaling act in concert to mount an effective response against virus infection, with a particular focus on the potential role of stress granules in the coordination of antiviral signaling cascades.