A prosthetic heart valve system, comprising: an expandable prosthetic heart valve having a constricted diameter and an expanded diameter; a delivery catheter having a distal end on or in which the prosthetic heart valve is mounted; a pinch device separate from the prosthetic heart valve that has an expanded state defining an annular frame formed around a central axis and having peaks (30, 32, 34) and valleys (40, 42, 44) extending in opposite axial directions around its periphery, the pinch device including an inner body, the pinch device in its expanded state being sized slightly smaller than the expanded diameter of the prosthetic heart valve, the pinch device having a plurality of buckles integrated with the inner body; and an access system including a proximal handle and a distal access sheath, the handle and sheath defining a common lumen sized for passage therethrough of the distal end of the delivery catheter with the prosthetic heart valve in its constricted diameter thereon, the access system including a plurality of deployment arms each coupled to one of the buckles of the pinch device, wherein at least one of the sheath and the plurality of deployment arms is axially movable relative to the other, wherein the pinch device is positioned, prior to delivery, in a constricted state within a distal end of the access sheath and distal with respect to the distal end of the delivery catheter, such that the pinch device can be expelled from the access sheath and self-expand prior to expansion of the prosthetic heart valve, the proximal handle having an advancement mechanism for axially displacing the deployment arms and/or retracting the sheath, and a release mechanism for decoupling each deployment arm from the pinch device, the advancement mechanism comprising a proximal grip portion slidably mounted over a distal housing of the proximal handle in a telescoping fashion, and wherein the system is configured such that the distal access sheath can be introduced into the heart and advanced so that the distal end thereof is proximate a native heart valve, whereupon the pinch device can be expelled therefrom and positioned around native heart valve leaflets and the delivery catheter can be advanced to position the prosthetic heart valve within the native heart valve leaflets such that expansion of the prosthetic heart valve pinches the native heart valve leaflets between the prosthetic heart valve and pinch device, wherein the release mechanism includes a filament extending from the proximal handle to a distal end of each deployment arm that nominally locks the deployment arm to the corresponding buckle, and an end sleeve on the proximal grip portion to which each filament is attached, wherein relative axial movement of the end sleeve with respect to the proximal grip portion pulls the filaments in a proximal direction. an expandable prosthetic heart valve having a constricted diameter and an expanded diameter; a delivery catheter having a distal end on or in which the prosthetic heart valve is mounted; a pinch device separate from the prosthetic heart valve that has an expanded state defining an annular frame formed around a central axis and having peaks (30, 32, 34) and valleys (40, 42, 44) extending in opposite axial directions around its periphery, the pinch device including an inner body, the pinch device in its expanded state being sized slightly smaller than the expanded diameter of the prosthetic heart valve, the pinch device having a plurality of buckles integrated with the inner body; and an access system including a proximal handle and a distal access sheath, the handle and sheath defining a common lumen sized for passage therethrough of the distal end of the delivery catheter with the prosthetic heart valve in its constricted diameter thereon, the access system including a plurality of deployment arms each coupled to one of the buckles of the pinch device, wherein at least one of the sheath and the plurality of deployment arms is axially movable relative to the other, wherein the pinch device is positioned, prior to delivery, in a constricted state within a distal end of the access sheath and distal with respect to the distal end of the delivery catheter, such that the pinch device can be expelled from the access sheath and self-expand prior to expansion of the prosthetic heart valve, the proximal handle having an advancement mechanism for axially displacing the deployment arms and/or retracting the sheath, and a release mechanism for decoupling each deployment arm from the pinch device, the advancement mechanism comprising a proximal grip portion slidably mounted over a distal housing of the proximal handle in a telescoping fashion, and wherein the system is configured such that the distal access sheath can be introduced into the heart and advanced so that the distal end thereof is proximate a native heart valve, whereupon the pinch device can be expelled therefrom and positioned around native heart valve leaflets and the delivery catheter can be advanced to position the prosthetic heart valve within the native heart valve leaflets such that expansion of the prosthetic heart valve pinches the native heart valve leaflets between the prosthetic heart valve and pinch device, wherein the release mechanism includes a filament extending from the proximal handle to a distal end of each deployment arm that nominally locks the deployment arm to the corresponding buckle, and an end sleeve on the proximal grip portion to which each filament is attached, wherein relative axial movement of the end sleeve with respect to the proximal grip portion pulls the filaments in a proximal direction.