Leishmania species are the causative agents of leishmaniasis, a neglected tropical disease. These parasitic protozoans are usually transmitted between vertebrate hosts by the bite of blood sucking female phlebotomine sand flies. This review focuses on the two parasites causing most human visceral leishmaniasis (VL), which leads to substantial health problems or death for up to 400,000 people per year. Except for travel cases, Leishmania donovani infections are restricted to the (sub-)tropics of Asia and Africa, where transmission is mostly anthroponotic, while Leishmania infantum occurs in the drier parts of Latin America as well as in the Mediterranean climate regions of the Old World, with the domestic dog serving as the main reservoir host. The prevalence of VL caused by L. infantum has been declining where living standards have improved. In contrast, infections of L. donovani continue to cause VL epidemics in rural areas on the Indian subcontinent and in East Africa. The current review compares and contrasts these continental differences and suggests priorities for basic and applied research that might improve VL control. Transmission cycles, pathogenesis, diagnosis, treatment and prognosis, prevention (including vector control), surveillance, transmission modeling, and international control efforts are all reviewed. Most case detection is passive, and so routine surveillance does not usually permit accurate assessments of any changes in the incidence of VL. Also, it is not usually possible to estimate the human inoculation rate of parasites by the sand fly vectors because of the limitations of survey methods. Consequently, transmission modeling rarely passes beyond the proof of principle stage, and yet it is required to help develop risk factor analysis for control programs. Anthroponotic VL should be susceptible to elimination by rapid case detection and treatment combined with local vector control, and one of the most important interventions may well be socioeconomic development.