An account is given of work published during the past 10 years incriminating species of phlebotomine sandflies as vectors of Leishmania species which infect man. An assessment is made of the degrees of certainty of the vectorial roles of eighty-one species and subspecies of sandflies (thirty-seven Old World and forty-four New World) in the transmission of twenty-nine leishmanial parasites of mammals. At least one species of sandfly is considered to be a proven vector of each of ten parasites. Of the eighty-one sandfly taxa, evidence is judged to be sufficient to incriminate nineteen as proven vectors (eleven Phlebotomus species and eight Lutzomyia species or subspecies) and evidence for a further fourteen (nine Phlebotomus species and five Lutzomyia species or subspecies) is considered to be strong. The suggested criteria for incrimination of a vector are anthropophily and common infection with the same leishmanial parasite as that found in man in the same place. More weight should be given to natural infections persisting after the digestion of a bloodmeal than those in the presence of blood. Supporting evidence is a concordance in the distribution of the fly and the disease in man, proof that the fly feeds regularly on the reservoir host, a flourishing development of the parasite in infected flies and the experimental transmission of the parasite by the bite of the fly.