A first step in primary disease prevention is identifying common, modifiable risk factors that contribute to a significant proportion of disease development. Infant respiratory viral infection and childhood asthma are the most common acute and chronic diseases of childhood, respectively. Common clinical features and links between these diseases have long been recognized, with early-life respiratory syncytial virus (RSV) and rhinovirus (RV) lower respiratory tract infections (LRTIs) being strongly associated with increased asthma risk. However, there has long been debate over the role of these respiratory viruses in asthma inception. In this article, we systematically review the evidence linking early-life RSV and RV LRTIs with asthma inception and whether they could therefore be targets for primary prevention efforts.