The Asian vinegar fly species Drosophila suzukii (spotted wing Drosophila or SWD) has emerged as an important invasive insect pest of small and stone fruits in both the Americas and Europe since the late 2000’s. While research efforts have rapidly progressed in Asia, North America, and Europe over the past 5 years, important new insights may be gained in comparing and contrasting findings across areas affected by SWD. In this review, we explore common themes in the invasion biology of SWD by examining: (1) its biology and current pest status in endemic and recently invaded regions; (2) current efforts and future research needs for the development of predictive models for its geographic expansion; and (3) prospects for both natural and classical (= importation) biological control of SWD in invaded habitats, with emphasis on the role of hymenopteran parasitoids. We conclude that particularly fruitful areas of research include fundamental studies of its overwintering, host-use, and dispersal capabilities; as well as applied studies of alternative, cost-effective management techniques to complement insecticide use within the integrated pest management (IPM) framework. Finally, we emphasize that outreach and extension efforts are critical to effective SWD pest management by highlighting successful strategies and insights gained from various geographic regions.