Aortic disease is a significant cause of death in developed countries. The most common forms of aortic disease are aneurysm, dissection, atherosclerotic occlusion and ageing-induced stiffening. The microstructure of the aortic tissue has been studied with great interest, because alteration of the quantity and/or architecture of the connective fibres (elastin and collagen) within the aortic wall, which directly imparts elasticity and strength, can lead to the mechanical and functional changes associated with these conditions. This review article summarizes the state of the art with respect to characterization of connective fibre microstructure in the wall of the human aorta in ageing and disease, with emphasis on the ascending thoracic aorta and abdominal aorta where the most common forms of aortic disease tend to occur.