Virus invasion triggers host immune responses, in particular, innate immune responses. Pathogen‐associated molecular patterns of viruses (such as dsRNA, ssRNA, or viral proteins) released during virus replication are detected by the corresponding pattern‐recognition receptors of the host, and innate immune responses are induced. Through production of type‐I and type‐III interferons as well as various other cytokines, the host innate immune system forms the frontline to protect host cells and inhibit virus infection. Not surprisingly, viruses have evolved diverse strategies to counter this antiviral system. In this review, we discuss the multiple strategies used by proteases of positive‐sense single‐stranded RNA viruses of the families Picornaviridae, Coronaviridae, and Flaviviridae, when counteracting host innate immune responses.