Viral RNA-dependent RNA polymerases (RdRps) play a central role not only in viral replication, but also in the genetic evolution of viral RNAs. After binding to an RNA template and selecting 5'-triphosphate ribonucleosides, viral RdRps synthesize an RNA copy according to Watson-Crick base-pairing rules. The copy process sometimes deviates from both the base-pairing rules specified by the template and the natural ribose selectivity and, thus, the process is error-prone due to the intrinsic (in)fidelity of viral RdRps. These enzymes share a number of conserved amino-acid sequence strings, called motifs A-G, which can be defined from a structural and functional point-of-view. A co-relation is gradually emerging between mutations in these motifs and viral genome evolution or observed mutation rates. Here, we review our current knowledge on these motifs and their role on the structural and mechanistic basis of the fidelity of nucleotide selection and RNA synthesis by Flavivirus RdRps.