A heart-valve delivery apparatus for delivering a prosthetic heart valve via a patient's vasculature, comprising: a first catheter having a first elongated shaft adapted to extend through the patient's vasculature; characterized in that the apparatus further comprises: a delivery sheath coupled to a distal end of the first shaft; a second catheter comprising a second, elongated flexible torque shaft extending within the first shaft of the first catheter, the torque shaft having a distal end portion adapted to be coupled to the prosthetic valve; and a valve-retaining mechanism for coupling the second catheter to the valve, wherein the sheath is configured to receive the valve in a radially compressed state when coupled to the distal end portion of the torque shaft for delivery to the heart through the patient's vasculature; and wherein rotation of the torque shaft relative to the first shaft and the sheath is effective to cause longitudinal movement of the sheath relative to the torque shaft and the valve to retract the sheath and deploy the valve from an open distal end of the sheath for deployment in the heart, the valve-retaining mechanism configured to form a releasable connection between the valve and the second catheter, which connection can be released after the valve is deployed from the sheath. a first catheter having a first elongated shaft adapted to extend through the patient's vasculature; characterized in that the apparatus further comprises: a delivery sheath coupled to a distal end of the first shaft; a second catheter comprising a second, elongated flexible torque shaft extending within the first shaft of the first catheter, the torque shaft having a distal end portion adapted to be coupled to the prosthetic valve; and a valve-retaining mechanism for coupling the second catheter to the valve, wherein the sheath is configured to receive the valve in a radially compressed state when coupled to the distal end portion of the torque shaft for delivery to the heart through the patient's vasculature; and wherein rotation of the torque shaft relative to the first shaft and the sheath is effective to cause longitudinal movement of the sheath relative to the torque shaft and the valve to retract the sheath and deploy the valve from an open distal end of the sheath for deployment in the heart, the valve-retaining mechanism configured to form a releasable connection between the valve and the second catheter, which connection can be released after the valve is deployed from the sheath. a delivery sheath coupled to a distal end of the first shaft; a second catheter comprising a second, elongated flexible torque shaft extending within the first shaft of the first catheter, the torque shaft having a distal end portion adapted to be coupled to the prosthetic valve; and a valve-retaining mechanism for coupling the second catheter to the valve, wherein the sheath is configured to receive the valve in a radially compressed state when coupled to the distal end portion of the torque shaft for delivery to the heart through the patient's vasculature; and wherein rotation of the torque shaft relative to the first shaft and the sheath is effective to cause longitudinal movement of the sheath relative to the torque shaft and the valve to retract the sheath and deploy the valve from an open distal end of the sheath for deployment in the heart, the valve-retaining mechanism configured to form a releasable connection between the valve and the second catheter, which connection can be released after the valve is deployed from the sheath.