The genus Flavivirus comprises numerous, small, single positive-stranded RNA viruses, many of which are important human pathogens. To store all the information required for their successful propagation, flaviviruses use discrete structural genomic RNA elements to code for functional information by the establishment of dynamic networks of long-range RNA–RNA interactions that promote specific folding. These structural elements behave as true cis-acting, non-coding RNAs (ncRNAs) and have essential regulatory roles in the viral cycle. These include the control of the formation of subgenomic RNAs, known as sfRNAs, via the prevention of the complete degradation of the RNA genome. These sfRNAs are important in ensuring viral fitness. This work summarizes our current knowledge of the functions performed by the genome conformations and the role of RNA–RNA interactions in these functions. It also reviews the role of RNA structure in the production of sfRNAs across the genus Flavivirus, and their existence in related viruses.