Coronaviruses use an RNA-dependent RNA polymerase (RdRp) to replicate and express their genome. The RdRp associates with additional non-structural proteins (nsps) to form a replication-transcription complex (RTC) that carries out RNA synthesis, capping and proofreading. However, the structure of the RdRp long remained elusive, thus limiting our understanding of coronavirus genome expression and replication. Recently, the cryo-electron microscopy structure of SARS-CoV-1 RdRp was reported. Driven by the ongoing COVID-19 pandemic, structural data on the SARS-CoV-2 polymerase and associated factors has since emerged at an unprecedented pace, with almost twenty structures released to date. This review provides an overview of the currently available coronavirus RdRp structures and outlines how they have, together with functional studies, led to a molecular understanding of the viral polymerase, its interactions with accessory factors and the mechanisms by which promising antivirals may inhibit coronavirus replication.