Methods are described herein for delivering a replacement mitral valve to a native mitral valve location. In one method, ventricular anchors of the replacement mitral valve are released and allowed to reverse orientation while positioned in the left atrium of a human heart. After reversing orientation, the ventricular anchors extend in a generally proximal direction. The ventricular anchors can then be advanced through the mitral annulus into the left ventricle and then moved back toward the left atrium to capture native mitral valve leaflets between the main body and the ventricular anchors of the replacement mitral valve. In one modification, the ventricular anchors are allowed to reverse orientation at a level adjacent the mitral annulus. The implantation methods described herein are preferably performed via a transseptal delivery approach or a transapical delivery approach.