Invasive species are recognised as one of the most important, growing threat to food biosecurity, causing a significant economic loss in agricultural systems. Despite their damaging effect, they are attractive models for the study of evolution and adaptation in newly colonised environments. Currently, the global climate represents one key potential stressors to impact the food biosecurity because of its influence in the distribution and change in the abundance of agricultural pests. The tephritid fruit flies (Diptera: Tephritidae) contain some of the most successful invaders and most devastating agricultural pests recognised worldwide. Among them, the Mediterranean fruit fly Ceratitis capitata and the South American fruit flies in the genus Anastrepha are particularly important for crop production. Insecticides have been used extensively for their control. This thesis investigates factors that are related to invasiveness in these species, in order to provide novel information that will ultimately improve management control methods. First, environmental niche modelling was used to determine the influence of climate change in the potential habitat distribution of C. capitata, predicting both polewards expansion as well as greater connectivity. Next, historical global dispersal patterns of the medfly over the past two centuries were investigated using molecular and genetic approaches. In Chapter 4, different attempts to identify the point mutation G328A Ccace2 gene that confers resistance to insecticides were assessed at local and intercontinental scale, in part by studying museum specimens from before and after the use of pesticides. Additionally, to improve genetic knowledge of this invasive species, the mitogenome of different species of Anastrepha were sequenced and analysed together with others tephritid. This investigation provides crucial information revealing the evolutionary factors that influence the medfly’s successful invasions and will contribute to the development of evidence-driven pest management protocols, especially in the Americas, including the choice among different control methods as well as the establishment of quarantine procedures to interrupt colonisation routes.