The phytophagous insects of the Tephritidae family commonly referred to as "true fruit flies" offer different case histories of successful invasions. Mankind has played an important role in altering the distributions of some of the more polyphagous and oligophagous species. However, the question arises why only a few species have become major invaders. The understanding of traits underlying adaptation in different environments is a major topic in invasion biology. Being generalists or specialists, along the K-r gradient of the growth curve, make a difference in term of food resources exploitation and interspecies competition and displacement. The species of the genus Ceratitis are good examples of r-strategists. The genetic and biological data of the most notorious Ceratitis species, the Mediterranean fruit fly Ceratitis capitata (medfly), are reviewed to investigate the traits and behaviours that make the medfly an important invader. It can be learnt from medfly, that invasions in a modern global trade network tend to be due to multiple introductions. This fact allows a maintenance or enhancement of genetic variability in the adventive populations, which in turn increases their potential invasiveness. Our current knowledge of the medfly genome opens the way for future studies on functional genomics.