Flaviviruses such as dengue, Japanese encephalitis, West Nile, Yellow Fever and Zika virus, cause viral hemorrhagic fever and encephalitis in humans. However, antiviral therapeutics to treat or prevent flavivirus infections are not yet available. Thus, there is pressing need to develop therapeutics and vaccines that target flavivirus infections. All flaviviruses carry a positive-sense single-stranded RNA genome, which encodes ten proteins; three structural proteins form the virus shell, and seven nonstructural (NS) proteins are involved in replication of the viral genome. While all NS proteins (NS1, NS2A, NS2B, NS3, NS4A, NS4B, and NS5) are part of a functional membrane-bound replication complex, enzymatic activities required for flaviviral replication reside in only two NS proteins, NS3 and NS5. NS3 functions as a protease, helicase, and triphosphatase, and NS5 as a capping enzyme, methyltransferase, and RNA-dependent RNA polymerase. In this chapter, we provide an overview of viral replication focusing on the structure and function of NS3 and NS5 replicases. We further describe strategies and examples of current efforts to identify potential flavivirus inhibitors against NS3 and NS5 enzymatic activities that can be developed as therapeutic agents to combat flavivirus infections.