Emerging and re-emerging mosquito-borne viral diseases impose a significant burden on global public health. The most common mosquito-borne viruses causing recent epidemics include flaviviruses in the family Flaviviridae, including Dengue virus (DENV), Zika virus (ZIKV), Japanese encephalitis virus (JEV) and West Nile virus (WNV) and Togaviridae viruses, such as chikungunya virus (CHIKV). Several factors may have contributed to the recent re-emergence and spread of mosquito-borne viral diseases. Among these important causes are the evolution of mosquito-borne viruses and the genetic mutations that make them more adaptive and virulent, leading to widespread epidemics. RNA viruses tend to acquire genetic diversity due to error-prone RNA-dependent RNA polymerases, thus promoting high mutation rates that support adaptation to environmental changes or host immunity. In this review, we discuss recent findings on the adaptive evolution of mosquito-borne viruses and their impact on viral infectivity, pathogenicity, vector fitness, transmissibility, epidemic potential and disease emergence.