An aortic aneurysm is a permanent and localized dilatation of the aorta resulting from an irreversible loss of structural integrity of the aortic wall. The infrarenal segment of the abdominal aorta is the most common site of aneurysms; however, they are also common in the ascending and descending thoracic aorta. Many cases remain undetected because thoracic aortic aneurysms (TAAs) are usually asymptomatic until complications such as aortic dissection or rupture occurs. Clinical estimates of rupture potential and dissection risk, and thus interventional planning for TAAs, are currently based primarily on the maximum diameter and growth rate. The growth rate is calculated from maximum diameter measurements at two subsequent time points; however, this measure cannot reflect the complex changes of vessel wall morphology and local areas of weakening that underline the strong regional heterogeneity of TAA. Due to the high risks associated with both open and endovascular repair, an intervention is only justified if the risk for aortic rupture or dissection exceeds the interventional risks. Consequently, TAAs clinical management remains a challenge, and new methods are needed to better identify patients for elective repair. We reviewed the pathophysiology of TAAs and the role of mechanical stresses and mathematical growth models in TAA management; as a proof of concept, we applied a multiscale biomechanical analysis to a case study of TAA.