Coronaviruses use an RNA-dependent RNA polymerase to replicate and transcribe their RNA genome. The structure of the SARS-CoV-2 polymerase was determined by cryo-electron microscopy within a short time in spring 2020. The structure explains how the viral enzyme synthesizes RNA and how it replicates the exceptionally large genome in a processive manner. The most recent structure-function studies further reveal the mechanism of polymerase inhibition by remdesivir, an approved drug for the treatment of COVID-19.