Coronaviruses (CoVs) belong to a large family of zoonotic supercapsid viruses, including about 40 species of RNA-containing viruses with several strains capable of causing damage to the lungs and respiratory tract. The severe acute respiratory syndrome coronavirus (SARS-CoV) was responsible for the worldwide SARS outbreak in 2003. The rapid global spread of SARS-CoV-2 has been the cause of significant health concerns and thousands of deaths in 2019-2020 and outlined the need for novel antivirals. The present review is devoted to the development of effective and selective nucleoside drugs for the treatment of coronavirus infections. To date, about half of antivirals have been created based on nucleosides. The majority of drugs based on nucleosides have been approved by FDA. This indicates a fruitful area for the development of novel antivirals based on nucleosides. The review describes the main features of pathogenic SARS-CoV, MERS-CoV, and SARS-CoV-2 strains, presents their comparison, considers promising approaches to creating nucleoside drugs for the treatment of coronavirus infections and provides a systematic evaluation of all the known nucleoside derivatives, which inhibit the reproduction of coronaviruses in cells. To date, two known nucleoside drugs (Remdesivir, Favipiravir) have been recommended for the treatment of SARS-CoV-2 infection and nine hit compounds based on nucleosides and their analogues have been found, one of which efficiently suppressing SARS-CoV-2 replication and eight others inhibiting SARS-CoV replication.