The genus Flavivirus comprises a large number of small, positive-sense single-stranded, RNA viruses able to replicate in the cytoplasm of certain arthropod and/or vertebrate host cells. The genus, which has some 70 member species, includes a number of emerging and re-emerging pathogens responsible for outbreaks of human disease around the world, such as the West Nile, dengue, Zika, yellow fever, Japanese encephalitis, St. Louis encephalitis, and tick-borne encephalitis viruses. Like other RNA viruses, flaviviruses have a compact RNA genome that efficiently stores all the information required for the completion of the infectious cycle. The efficiency of this storage system is attributable to supracoding elements, i.e., discrete, structural units with essential functions. This information storage system overlaps and complements the protein coding sequence and is highly conserved across the genus. It therefore offers interesting potential targets for novel therapeutic strategies. This review summarizes our knowledge of the features of flavivirus genome functional RNA domains. It also provides a brief overview of the main achievements reported in the design of antiviral nucleic acid-based drugs targeting functional genomic RNA elements.