A valve prosthesis (700, 800, 1300, 1400) comprising: a valve frame comprising an annulus element, the annulus element (706, 806, 1306, 1406) configured for positioning at or near a native heart valve annulus; and a skirt (810, 1310) attached to said annulus element and extending through an opening of said native heart valve, characterized by: said skirt (810, 1310) being movable between an open configuration and a closed configuration in conjunction with a native function of leaflets of said native heart valve; and further comprising at least two first anchoring extensions (702, 802, 1302, 1402) attached to the annulus element (706, 806, 1306, 1406), the first anchoring extensions (702, 802, 1302, 1402) configured and circumferentially arranged to extend from an atrium, into a ventricle, and through said native heart valve at ends of commissures of said native heart valve between said leaflets of said native heart valve, where leaflets of said native heart valve meet, without deforming a native configuration of said leaflets of said native heart valve, wherein said first anchoring extensions are reinforcing members extending downwardly through the interior of a valve skirt to support said skirt and such first anchoring extensions are configured to prevent prolapse of the skirt into the atrium. a valve frame comprising an annulus element, the annulus element (706, 806, 1306, 1406) configured for positioning at or near a native heart valve annulus; and a skirt (810, 1310) attached to said annulus element and extending through an opening of said native heart valve, characterized by: said skirt (810, 1310) being movable between an open configuration and a closed configuration in conjunction with a native function of leaflets of said native heart valve; and further comprising at least two first anchoring extensions (702, 802, 1302, 1402) attached to the annulus element (706, 806, 1306, 1406), the first anchoring extensions (702, 802, 1302, 1402) configured and circumferentially arranged to extend from an atrium, into a ventricle, and through said native heart valve at ends of commissures of said native heart valve between said leaflets of said native heart valve, where leaflets of said native heart valve meet, without deforming a native configuration of said leaflets of said native heart valve, wherein said first anchoring extensions are reinforcing members extending downwardly through the interior of a valve skirt to support said skirt and such first anchoring extensions are configured to prevent prolapse of the skirt into the atrium. said skirt (810, 1310) being movable between an open configuration and a closed configuration in conjunction with a native function of leaflets of said native heart valve; and further comprising at least two first anchoring extensions (702, 802, 1302, 1402) attached to the annulus element (706, 806, 1306, 1406), the first anchoring extensions (702, 802, 1302, 1402) configured and circumferentially arranged to extend from an atrium, into a ventricle, and through said native heart valve at ends of commissures of said native heart valve between said leaflets of said native heart valve, where leaflets of said native heart valve meet, without deforming a native configuration of said leaflets of said native heart valve, wherein said first anchoring extensions are reinforcing members extending downwardly through the interior of a valve skirt to support said skirt and such first anchoring extensions are configured to prevent prolapse of the skirt into the atrium.