Positive-sense single-stranded RNA (+ssRNA) viruses comprise many (re-)emerging human pathogens that pose a public health problem. Our innate immune system and in particular the interferon response form the important first line of defense against these viruses. Given their genetic flexibility, these viruses have therefore developed multiple strategies to evade the innate immune response in order to optimize their replication capacity. Already many molecular mechanisms of innate immune evasion by +ssRNA viruses have been identified. However, research addressing the effect of host innate immune evasion on the pathology caused by the viral infection is less prevalent in literature, though very relevant and interesting. Since interferons have been implicated in inflammatory diseases and immunopathology in addition to their protective role in infection, the influence of antagonizing the immune response may have an ambiguous effect on the clinical outcome of the viral disease. Therefore, this review discusses what is currently known about the role of interferons and host immune evasion in the pathogenesis of emerging viruses belonging to the coronaviruses, alphaviruses and flaviviruses.