RNA viruses can cause severe diseases such as dengue, Lassa, chikungunya and Ebola. Many of these viruses can only be propagated under high containment levels, necessitating the development of low containment surrogate systems such as subgenomic replicons and minigenome systems. Replicons are self-amplifying recombinant RNA molecules expressing proteins sufficient for their own replication but which do not produce infectious virions. Replicons can persist in cells and are passed on during cell division, enabling quick, efficient and high-throughput testing of drug candidates that act on viral transcription, translation and replication. This review will explore the history and potential for drug discovery of hepatitis C virus, dengue virus, respiratory syncytial virus, Ebola virus and norovirus replicon and minigenome systems.