Chikungunya and Zika viruses, both transmitted by mosquito vectors, have globally re-emerged over for the last 60 years and resulted in crucial social and economic concerns. Presently, there is no specific antiviral agent or vaccine against these debilitating viruses. Understanding viral–host interactions is needed to develop targeted therapeutics. However, there is presently limited information in this area. In this review, we start with the updated virology and replication cycle of each virus. Transmission by similar mosquito vectors, frequent co-circulation, and occurrence of co-infection are summarized. Finally, the targeted host proteins/factors used by the viruses are discussed. There is an urgent need to better understand the virus–host interactions that will facilitate antiviral drug development and thus reduce the global burden of infections caused by arboviruses.