Thoracic endovascular aortic repair (TEVAR) is rapidly emerging as an important treatment option for several indications, and it would not be unreasonable to predict that endograft treatment may well become the predominant form of therapy for many, if not the majority, of patients. However, several unresolved issues remain, and the need for further improvements and technological refinements will not cease any time soon. Ranking high among these issues are the challenges related to endovascular access and aortic branch management, which constitute the main focus of this review. Achieving safe and successful endovascular access for introduction and deployment of the stent-graft device is a crucially important and often challenging step during TEVAR, but arterial injury has been, and continues to be, an all-too-common occurrence to this day. A clear understanding of the relevant issues and available technical solutions can go a long way toward preventing such catastrophes. A preponderance of thoracic aortic pathologies tend to develop adjacent to or within the branched segments. It is therefore not surprising that branch management issues have risen to the top of the entire TEVAR field. Debranching and vessel relocation techniques have added a whole new dimension to the therapy because they can expand or create suitable landing zones proximally and distally, thereby broadening the applicability of endograft technologies to a much larger number of patients.