Insect pests have a widespread negative impact on livestock production, resulting in large economic losses. Monitoring and surveillance of pest species are fundamental to manage their populations and reduce the damage they inflict on livestock. In addition, resistance to pest control methods, such as the use of insecticides, is becoming an increasingly important issue. Inferring population structure, the phylogeographic pattern of pest species, and the connectivity among populations is key to understanding migration patterns, which can be used to delineate area-wide pest surveillance and management schemes such as the Sterile Insect Technique (SIT). This review provides a summary of phylogeographic patterns of the New World screwworm (NWS) fly, Cochliomyia hominivorax Coquerel, a myiasis-causing fly that leads to significant losses in livestock production, based on molecular markers and the monitoring of insecticide resistance to improve its management. The species’ current geographic distribution comprises most of the Neotropical region, having been eradicated in North and Central America after area-wide integration of the SIT with other methods. Introducing similar management programmes in South America and the Caribbean could be a strategic alternative to the permanent and exclusive use of insecticides, which has a negative environmental impact and is a growing challenge because of increasing resistance development in NWS. Such an area-wide approach requires NWS population delineation at regional and geographic scales, and the monitoring of mutations that are involved in insecticide resistance in natural populations.