Rapid changes in the viral genome allow viruses to evade threats posed by the host immune response or antiviral drugs, and can lead to viral persistence in the host cells. RNA-dependent RNA polymerase (RdRp) is an essential enzyme in RNA viruses, which is involved in RNA synthesis through the formation of phosphodiester bonds. Therefore, in RNA viral infections such as SARS-CoV-2, RdRp could be a crucial therapeutic target. The present review discusses the promising application of RdRp inhibitors, previously approved or currently being tested in human clinical trials, in the treatment of RNA virus infections. Nucleoside inhibitors (NIs) bind to the active site of RdRp, while nonnucleoside inhibitors (NNIs) bind to allosteric sites. Given the absence of highly effective drugs for the treatment of COVID-19, the discovery of an efficient treatment for this pandemic is an urgent concern for researchers around the world. We review the evidence for molnupiravir (MK-4482, EIDD-2801), an antiviral drug originally designed for Alphavirus infections, as a potential preventive and therapeutic agent for the management of COVID-19. At the beginning of this pandemic, molnupiravir was in preclinical development for seasonal influenza. When COVID-19 spread dramatically, the timeline for development was accelerated to focus on the treatment of this pandemic. Real time consultation with regulators took place to expedite this program. We summarize the therapeutic potential of RdRp inhibitors, and highlight molnupiravir as a new small molecule drug for COVID-19 treatment.