Viral infection triggers the activation of antiviral innate immune responses in mammalian cells. Viral RNA in the cytoplasm activates signaling pathways that result in the production of interferons (IFNs) and IFN-stimulated genes. Some viral infections have been shown to induce cytoplasmic granular aggregates similar to the dynamic ribonucleoprotein aggregates termed stress granules (SGs), suggesting that these viruses may utilize this stress response for their own benefit. By contrast, some viruses actively inhibit SG formation, suggesting an antiviral function for these structures. We review here the relationship between different viral infections and SG formation. We examine the evidence for antiviral functions for SGs and highlight important areas of inquiry towards understanding cellular stress responses to viral infection.