A system for delivering a collapsible and re-expandable prosthetic heart valve into a patient includes a valve support structure (140) around which the valve (10) is disposed in a collapsed condition. A sheath structure (110) surrounds the collapsed valve, but can be moved relative to the valve to uncover it for expansion at the desired implant site in the patient. The sheath structure may be variously mounted and moved to deploy the valve in various ways. For example, the sheath structure may include multiple parts, each of which can be moved separately to separately deploy various parts of the valve. The apparatus may have other aspects, such as the ability to reverse deployment of the valve, the ability to pass other instrumentation through the valve delivery apparatus, the ability to be smoothly withdrawn from the patient after deployment of the valve, etc.
