Zebrafish possess a highly developed immune system that is remarkably similar to the human one. Therefore, it is expected that the majority of the signalling pathways and molecules involved in the immune response of mammals exist and behave similarly in fish. The innate antiviral response depends on the recognition of viral components by host cells. Pattern recognition receptors initiate antimicrobial defence mechanisms via several well-conserved signalling pathways. In this paper, we review current knowledge of the antiviral innate immune response in zebrafish by considering the main molecules that have been characterized and the infection models used for the in vivo study of the antiviral innate immune response. We next summarize published studies in which larval and adult zebrafish were used to study viral diseases of fish, then provide a similar review of studies of human viral diseases in zebrafish and experience with antiviral drug screening in this model organism.