Respiratory viruses cause disease in humans characterized by an abrupt onset of symptoms. Studies in humans and animal models have shown that symptoms are not immediate and appear days or even weeks after infection. Since the initial symptoms are a manifestation of virus recognition by elements of the innate immune response, early virus replication must go largely undetected. The interval between infection and the emergence of symptoms is called the incubation period and is widely used as a clinical score. While incubation periods have been described for many virus infections the underlying mechanism for this asymptomatic phase has not been comprehensively documented. Here we review studies of the interaction between human pathogenic respiratory RNA viruses and the host with a particular emphasis on the mechanisms used by viruses to inhibit immunity. We discuss the concept of the “stealth phase”, defined as the time between infection and the earliest detectable inflammatory response. We propose that the “stealth phase” phenomenon is primarily responsible for the suppression of symptoms during the incubation period and results from viral antagonism that inhibits major pathways of the innate immune system allowing an extended time of unhindered virus replication.