Untreated thoracoabdominal aortic aneurysms are associated with an exceedingly high mortality rate, and surgery carries a high complication rate. Crawford's classification system of thoracoabdominal aortic aneurysms describes aneurysm morphology and stratifies patients on the basis of risk of major postoperative complications including mortality, spinal cord injury, and renal failure. Computed tomography and magnetic resonance angiography are essential for classifying thoracoabdominal aortic aneurysms and identifying other important features that impact prognosis and surgical management. Four-dimensional flow-sensitive magnetic resonance imaging is an emerging technique that may help predict complications and further impact timing of intervention.