The World Health Organization estimates that the yearly number of dengue cases averages 390 million. This mosquito-borne virus disease is endemic in over 100 countries and will probably continue spreading, given the observed trend in global warming. So far, there is no antiviral drug available against dengue, but a vaccine has been recently marketed. Dengue virus also serves as a prototype for the study of other pathogenic flaviviruses that are emerging, like West Nile virus and Zika virus. Upon viral entry into the host cell and fusion of the viral lipid membrane with the endosomal membrane, the viral RNA is released and expressed as a polyprotein, that is then matured into three structural and seven non-structural (NS) proteins. The envelope, membrane and capsid proteins form the viral particle while NS1-NS2A-NS2B-NS3-NS4A-NS4B and NS5 assemble inside a cellular replication complex, which is embedded in endoplasmic reticulum (ER)-derived vesicles. In addition to their roles in RNA replication within the infected cell, NS proteins help the virus escape the host innate immunity and reshape the host-cell inner structure. This review focuses on recent progress in characterizing the structure and functions of NS5, a protein responsible for the replication and capping of viral RNA that represents a promising drug target.