Hepatitis C virus and related viruses in the Flaviviridae family (such as dengue virus, yellow fever virus or West Nile virus) are amongst the most important human pathogens, causing substantial morbidity and mortality world-wide. The production of viral progeny in Flaviviridae is orchestrated by the small, multifunctional core protein, which coats and condenses the viral genomic RNA during Nucleocapsid formation. In addition to their structural role, mounting experimental evidence links core proteins to viral persistence and pathogenesis, by virtue of their promiscuous interactions with host cell factors. In this review, we summarize the present knowledge about the structure of Flaviviridae core proteins and discuss the importance of flexible, intrinsically unstructured protein regions in viral assembly and hub formation in the virus-host protein-protein interaction network (infection network).