Viral triggering of the innate immune response in infected cells aims at delaying viral replication and prevents tissue spreading. Viral replication is delayed by host protein synthesis inhibition and infected cell apoptosis on one hand, while infection spreading is controlled by the synthesis of specific proteins like type-I interferons (IFNs) and pro-inflammatory cytokines on the other hand. How do these two apparent conflicting responses cooperate within the same infected cells to mount effective defenses against pathogens? What are the molecules or the complexes resolving this contradiction over time? Some recent studies reveal unanticipated connections between innate immunity and stress pathways, giving important clues on how the cellular responses are orchestrated to limit infection efficiently.