Worldwide, respiratory syncytial virus (RSV) causes severe disease in infants, the elderly, and immunocompromised people. No vaccine or effective antiviral treatment is available. RSV is a member of the non-segmented, negative-strand (NNS) group of RNA viruses and relies on its RNA-dependent RNA polymerase to transcribe and replicate its genome. Because of its essential nature and unique properties, the RSV polymerase has proven to be a good target for antiviral drugs, with one compound, ALS-8176, having already achieved clinical proof-of-concept efficacy in a human challenge study. In this article, we first provide an overview of the role of the RSV polymerase in viral mRNA transcription and genome replication. We then review past and current approaches to inhibiting the RSV polymerase, including use of nucleoside analogs and non-nucleoside inhibitors. Finally, we consider polymerase inhibitors that hold promise for treating infections with other NNS RNA viruses, including measles and Ebola.