Zika virus (ZIKV), discovered in the Zika Forest of Uganda in 1947, is a mosquito-borne flavivirus related to yellow fever, dengue and West Nile viruses. From its discovery until 2007, only sporadic ZIKV cases were reported, with mild clinical manifestations in patients. Therefore, little attention was given to this virus before epidemics in the South Pacific and the Americas that began in 2013. Despite a growing number of ZIKV studies in the past three years, many aspects of the virus remain poorly characterized, particularly the spectrum of species involved in its transmission cycles. Here, we review the mosquito and vertebrate host species potentially involved in ZIKV vector-borne transmission worldwide. We also provide an evidence-supported analysis regarding the possibility of ZIKV spillback from an urban cycle to a zoonotic cycle outside Africa, and we review hypotheses regarding recent emergence and evolution of ZIKV. Finally, we identify critical remaining gaps in the current knowledge of ZIKV vector-borne transmission.