Viruses infect all types of organisms, causing viral diseases, which are very common in humans. Since viruses use the metabolic pathways of their host cells to replicate, they are difficult to eradicate without affecting the cells. The most effective measures against viral infections are vaccinations and antiviral drugs, which selectively inhibit the viral replication cycle. Both methods have disadvantages, which requires the development of new approaches to the treatment of viral diseases. In the study of animal venoms, it was found that, in addition to toxicity, venoms exhibit other types of biological activity, including an antiviral one, the first mention of which dates back to middle of the last century, but detailed studies of their antiviral activity have been conducted over the past 15 years. The COVID-19 pandemic has reinforced these studies and several compounds with antiviral activity have been identified in venoms. Some of them are very active and can be considered as the basis for antiviral drugs. This review discusses recent antiviral studies, the found compounds with high antiviral activity, and the possible mechanisms of their action. The prospects for using the animal venom components to create antiviral drugs, and the expected problems and possible solutions are also considered.