The CLIMEX model was used to infer the climatic requirements of the Mediterranean fruit fly, Ceratitis capitata (Wiedemann), from the fruit fly’s observed geographical distribution in the Mediterranean region. The model indicated that the potential distribution was limited by cold to the north in Europe and by dryness in northern Africa and in the south of Spain and Portugal. The model was then used to estimate the potential geographical distribution of the species in Argentina and Australia. The results agreed with the observed distribution in Argentina and much of the historical distribution in Australia, but they did not agree with the present distribution in eastern Australia. In the latter region, another species of fruit fly, Bactrocera (Dacus) tryoni (Froggatt) has been credited with displacing C. capitata. Seasonal and year-to-year variation in climatic suitability was explored at three selected locations in Argentina. The results indicated that some detrimental effects of summer temperatures, or of extremes of precipitation, occurred in particular areas. Some of these limiting factors, especially dry stress, were prolonged enough to restrict the geographical distribution of medfly. However, when irrigation was included in the simulations, the detrimental effect of dryness was removed. Finally, a global risk map for medfly was produced, which highlights the areas at risk from this major quarantine pest.