Spatio-temporal modelling of the distributions of the leishmaniases and their sandfly vectors is reviewed in relation to climate change. Many leishmaniases are rural zoonoses, and so there is a foundation of descriptive ecology and qualitative risk assessment. Dogs are widespread reservoir hosts of veterinary importance. Recent statistical modelling has not always produced novel general conclusions, exemplifying the difficulty of applying models outside the original geographical region. Case studies are given for transmission cycles involving both cutaneous and visceral leishmaniasis in the Old World and the Americas. An important challenge is to integrate statistical spatial models based mainly on climate with more explanatory biological models. Ecological niche models pose difficulties because of the number of assumptions. A positive association has been reported between the El Niño cycle and the annual incidence of visceral leishmaniasis in Brazil, but more basic research is needed before tackling other climate-change scenarios, including leishmaniasis emergence in northern Europe.