The mosquito-borne arbovirus Zika virus (ZIKV, Flavivirus, Flaviviridae), has caused an outbreak impressive by its magnitude and rapid spread. First detected in Uganda in Africa in 1947, from where it spread to Asia in the 1960s, it emerged in 2007 on the Yap Island in Micronesia and hit most islands in the Pacific region in 2013. Subsequently, ZIKV was detected in the Caribbean, and Central and South America in 2015, and reached North America in 2016. Although ZIKV infections are in general asymptomatic or causing mild self-limiting illness, severe symptoms have been described including neurological disorders and microcephaly in newborns. To face such an alarming health situation, WHO has declared Zika as an emerging global health threat. This review summarizes the literature on the main vectors of ZIKV (sylvatic and urban) across all the five continents with special focus on vector competence studies.