Viruses exploit host metabolic and defence machinery for their own replication. The flaviviruses, which include Dengue (DENV), Yellow Fever (YFV), Japanese Encephalitis (JEV), West Nile (WNV) and Zika (ZIKV) viruses, infect a broad range of hosts, cells and tissues. Flaviviruses are largely transmitted by mosquito bites and humans are usually incidental, dead-end hosts, with the notable exceptions of YFV, DENV and ZIKV. Infection by flaviviruses elicits cellular responses including cell death via necrosis, pyroptosis (involving inflammation) or apoptosis (which avoids inflammation). Flaviviruses exploit these mechanisms and subvert them to prolong viral replication. The different effects induced by DENV, WNV, JEV and ZIKV are reviewed. Host cell surface proteoglycans (PGs) bearing glycosaminoglycan (GAG) polysaccharides — heparan/chondroitin sulfate (HS/CS) — are involved in initial flavivirus attachment and during the expression of non-structural viral proteins play a role in disease aetiology. Recent work has shown that ZIKV-infected cells are protected from cell death by exogenous heparin (a GAG structurally similar to host cell surface HS), raising the possibility of further subtle involvement of HS PGs in flavivirus disease processes. The aim of this review is to synthesize information regarding DENV, WNV, JEV and ZIKV from two areas that are usually treated separately: the response of host cells to infection by flaviviruses and the involvement of cell surface GAGs in response to those infections.