The optimal surgical treatment for extended thoracoabdominal aortic aneurysms (TAAAs) is still a matter of debate. The historical treatment is open repair (OR), but over the past fifteen years, endovascular strategies have gained widespread acceptance. Although several endovascular techniques have been described for the treatment of TAAAs, fenestrated and branched stent grafts (F/BEVARs) are the most frequently used and best documented. They have become the first-line treatment for both high- and moderate-risk surgical patients in most vascular centers. However, no randomized study comparing OR and F/BEVAR has been published, and decision-making is mainly based on the physician’s preference and/or hospital expertise. The objective of this manuscript is to provide an overview of current comparative data for OR and F/BEVAR.