The genus Enterovirus combines a portion of small (+)ssRNA-containing viruses and is divided into 10 species of true enteroviruses and three species of rhinoviruses. These viruses are causative agents of the widest spectrum of severe and deadly epidemic diseases of higher vertebrates, including humans. Their ubiquitous distribution and high pathogenicity motivate active search to counteract enterovirus infections. There are no sufficiently effective drugs targeted against enteroviral diseases, thus treatment is reduced to supportive and symptomatic measures. This makes it extremely urgent to develop drugs that directly affect enteroviruses and hinder their development and spread in infected organisms. In this review, we cover the classification of enteroviruses, mention the most common enterovirus infections and their clinical manifestations, and consider the current state of development of anti-enteroviral drugs. One of the most promising targets for such antiviral drugs is the viral Internal Ribosome Entry Site (IRES). The classification of these elements of the viral mRNA translation system is also examined.