Dengue virus is an important human pathogen that belongs to the Flaviviridae family. The viral genome is a single molecule of RNA of positive polarity that plays multiple roles during the viral life cycle. Besides encoding the viral proteins, the genome contains RNA structures that regulate different viral processes. An important feature of dengue and other flavivirus genomes is the presence of inverted complementary sequences at the ends of the molecule that mediate long-range RNA-RNA interaction and genome cyclization. Recent studies have demonstrated that alternative conformations of the genome are necessary for infectivity. In this review, we discuss the current understanding of the function of different RNA elements that modulate dengue virus replication and provide new ideas of how dynamic RNA structures participate in the viral processes.