The recent emergence and re-emergence of viral infections transmitted by vectors—Zika, chikungunya, dengue, Japanese encephalitis, West Nile, yellow fever and others—is a cause for international concern. Using as examples Zika, chikungunya and dengue, we summarise current knowledge on characteristics of the viruses and their transmission, clinical features, laboratory diagnosis, burden, history, possible causes of the spread and the expectation for future epidemics. Arboviruses are transmitted by mosquitoes, are of difficult diagnosis, can have surprising clinical complications and cause severe burden. The current situation is complex, because there is no vaccine for Zika and chikungunya and no specific treatment for the three arboviruses. Vector control is the only comprehensive solution available now and this remains a challenge because up to now this has not been very effective. Until we develop new technologies of control mosquito populations, the globalised and urbanised world we live in will remain vulnerable to the threat of successive arbovirus epidemics.