The family Flaviviridae comprises several major human pathogens including Hepatitis C virus (genus hepacivirus), yellow fever virus or dengue virus (genus flavivirus). The Flaviviridae genomes are made of a single stranded RNA segment that encodes seven non-structural proteins : NS1, NS2A, NS2B, NS3, NS4A, NS4B and NS5 in the flaviviruses like dengue virus and p7, NS2, NS3, NS4A, NS4B, NS5A and NS5B for Hepatitis C virus. These proteins are expressed during the intracellular part of the infectious cycle, where they participate in transcribing and replicating the viral genome in the context of a membrane-bound multi-protein complex named the replication complex. Several of these proteins are endowed with one or multiple enzymatic activities and represent important targets against which specific antiviral inhibitors have been developed, several of which are currently used for therapy. Here, we review our current understanding of the molecular basis for viral RNA transcription and replication, focusing on polymerases and protease-helicases.