The mosquito vector transmits arthropod-borne viruses (arboviruses) of medical importance, including Zika, dengue, and yellow fever viruses. Controlling mosquito populations remains the method of choice to prevent disease transmission. Novel mosquito control strategies based on genetically manipulating mosquitoes are being developed as additional tools to combat arbovirus transmission. Genetic control of mosquitoes includes two basic strategies: population suppression and population replacement. The former aims to eliminate mosquito populations while the latter aims to replace wild populations with engineered, pathogen-resistant mosquitoes. In this review, we outline suppression strategies being applied in the field, as well as current antiviral effector genes that have been characterized and expressed in transgenic for population replacement. We discuss cutting-edge gene drive technologies that can be used to enhance the inheritance of effector genes, while highlighting the challenges and opportunities associated with gene drives. Finally, we present currently available models that can estimate mosquito release numbers and time to transgene fixation for several gene drive systems. Based on the recent advances in genetic engineering, we anticipate that antiviral transgenic exhibiting gene drive will soon emerge; however, close monitoring in simulated field conditions will be required to demonstrate the efficacy and utility of such transgenic mosquitoes.