Compliant vascular grafts for implantation in the vasculature are provided. The compliant vascular grafts are designed to expand longitudinally and radially within a blood vessel, such as an artery, and is expected to be particularly well suited for treating aneurysms in challenging anatomy such as the thoracic aorta. The compliant vascular grafts preferably have an outer frame layer and an inner graft layer with a plurality of pleats to permit expansion.