Drosophila suzukii, a vinegar fly originated from Southeast Asia, has recently invaded western countries, and it has been recognized as an important threat of a wide variety of several commercial soft fruits. This review summarizes the current information about the biology and dispersal of D. suzukii and discusses the current status and prospects of control methods for the management of this pest. We highlight current knowledge and ongoing research on innovative environmental-friendly control methods with emphasis on the sterile insect technique (SIT) and the incompatible insect technique (IIT). SIT has been successfully used for the containment, suppression or even eradication of populations of insect pests. IIT has been proposed as a stand-alone tool or in conjunction with SIT for insect pest control. The principles of SIT and IIT are reviewed, and the potential value of each approach in the management of D. suzukii is analyzed. We thoroughly address the challenges of SIT and IIT, and we propose the use of SIT as a component of an area-wide integrated pest management approach to suppress D. suzukii populations. As a contingency plan, we suggest a promising alternative avenue through the combination of these two techniques, SIT/IIT, which has been developed and is currently being tested in open-field trials against Aedes mosquito populations. All the potential limiting factors that may render these methods ineffective, as well as the requirements that need to be fulfilled before their application, are discussed.