Emerging mosquito-borne viruses continue to cause serious health problems and economic burden among billions of people living in and near the tropical belt of the world. The highly invasive mosquito species Aedes aegypti and Aedes albopictus have successively invaded and expanded their presence as key vectors of Chikungunya virus, dengue virus, yellow fever virus, and Zika virus, and that has consecutively led to frequent outbreaks of the corresponding viral diseases. Of note, these two mosquito species have gradually adapted to the changing weather and environmental conditions leading to a shift in the epidemiology of the viral diseases, and facilitated their establishment in new ecozones inhabited by immunologically naive human populations. Many abilities of Ae. aegypti and Ae. albopictus, as vectors of significant arbovirus pathogens, may affect the infection and transmission rates after a bloodmeal, and may influence the vector competence for either virus. We highlight that many collaborating risk factors, for example, the global transportation systems may result in sporadic and more local outbreaks caused by mosquito-borne viruses related to Ae. aegypti and/or Ae. albopictus. Those local outbreaks could in synergy grow and produce larger epidemics with pandemic characters. There is an urgent need for improved surveillance of vector populations, human cases, and reliable prediction models. In summary, we recommend new and innovative strategies for the prevention of these types of infections.