Disclosed herein are representative embodiments of methods, apparatus, and systems used to deliver a prosthetic heart valve assembly. In embodiments, a prosthetic heart valve assembly, including a self-expandable support structure and a self-expanding heart valve, are advanced through the aortic arch of a patient using a delivery system. The support structure, which includes a plurality leaflet retaining arms, is at least partially expanded and positioned on or adjacent to the outflow side of the aortic valve. The prosthetic heart valve is positioned in the aortic valve. The prosthetic heart valve is expanded while it is within an interior of the support structure and while the support structure is positioned on or adjacent to the outflow side of the aortic valve, thereby causing one or more native leaflets of the aortic valve to be frictionally secured between the arms of the support structure and the expanded prosthetic heart valve.