Thoracic endovascular aortic repair (TEVAR) has emerged as a promising therapeutic alternative to conventional open aortic replacement but it requires suitable proximal landing zones for stent-graft anchoring. In patients in whom the distance between the LSA and aortic lesion is too short, extension of the landing zone can be obtained by covering the LSA’s origin with the endovascular stent graft. However, this maneuver has the potential to cause immediate and delayed neurological and vascular complications. Therefore, the management of LSA is still controversial, such as whether prophylactic LSA revascularization is needed and when, and how to perform a revascularization procedure? In this paper, the authors present the current situation and progress on the above issues.