Flaviviruses, such as dengue, Japanese encephalitis, tick-borne encephalitis, West Nile, yellow fever, and Zika viruses, are critically important human pathogens that sicken a staggeringly high number of humans every year. Most of these pathogens are transmitted by mosquitos, and not surprisingly, as the earth warms and human populations grow and move, their geographic reach is increasing. Flaviviruses are simple RNA-protein machines that carry out protein synthesis, genome replication, and virion packaging in close association with cellular lipid membranes. In this review, we examine the molecular biology of flaviviruses touching on the structure and function of viral components and how these interact with host factors. The latter are functionally divided into pro-viral and antiviral factors, both of which, not surprisingly, include many RNA binding proteins. In the interface between the virus and the hosts we highlight the role of a noncoding RNA produced by flaviviruses to impair antiviral host immune responses. Throughout the review, we highlight areas of intense investigation, or a need for it, and potential targets and tools to consider in the important battle against pathogenic flaviviruses.