The incidence and operations of thoracic and thoracoabdominal aortic aneurysms have significantly increased. The indications for repair are considered to be a diameter of 6 cm or more and 5.5 cm for patient groups with increased risk of rupture. Complex open surgical repair is associated with significant mortality and complication rates. Total or hybrid endovascular repair seems to reduce early postoperative complications and mortality. The endovascular approach has evolved to be a good and predominant alternative to open repair of these aneurysms for older and high-risk patients as well as for aneurysms with optimal morphological suitability. Notwithstanding, at present a complete paradigm shift from open to endovascular repair for all patients, especially those with complex aneurysms, cannot yet be established.