An implant for reshaping a native mitral valve of a heart, the implant comprising: a coiled anchor having a first end, a second end, and a central axis extending between the first and second ends, wherein the coiled anchor defines an inner space coaxial with the central axis and comprises: a first turn defining a central portion of the inner space having a first width; a second turn connected to the first turn at the first end of the coiled anchor, the second turn defining a portion of the inner space having a width that is smaller than the first width; and a third turn connected to the first turn at the second end of the coiled anchor, the third turn defining another portion of the inner space having a width that is smaller than the first width; wherein the coiled anchor is implantable at the native mitral valve with at least a portion of the first turn of the coiled anchor positioned in a left ventricle of the heart and around valve leaflets of the native mitral valve, a stent comprising an expandable stent frame configured to be expanded in the inner space of the coiled anchor; and a prosthetic valve comprising an expandable frame and housing a plurality of leaflets for controlling blood flow therethrough, wherein the prosthetic valve is expandable to a width that is at least the width of the stent when the stent is expanded, such that the prosthetic valve is configured to be held in the stent. a coiled anchor having a first end, a second end, and a central axis extending between the first and second ends, wherein the coiled anchor defines an inner space coaxial with the central axis and comprises: a first turn defining a central portion of the inner space having a first width; a second turn connected to the first turn at the first end of the coiled anchor, the second turn defining a portion of the inner space having a width that is smaller than the first width; and a third turn connected to the first turn at the second end of the coiled anchor, the third turn defining another portion of the inner space having a width that is smaller than the first width; wherein the coiled anchor is implantable at the native mitral valve with at least a portion of the first turn of the coiled anchor positioned in a left ventricle of the heart and around valve leaflets of the native mitral valve, a first turn defining a central portion of the inner space having a first width; a second turn connected to the first turn at the first end of the coiled anchor, the second turn defining a portion of the inner space having a width that is smaller than the first width; and a third turn connected to the first turn at the second end of the coiled anchor, the third turn defining another portion of the inner space having a width that is smaller than the first width; wherein the coiled anchor is implantable at the native mitral valve with at least a portion of the first turn of the coiled anchor positioned in a left ventricle of the heart and around valve leaflets of the native mitral valve, a stent comprising an expandable stent frame configured to be expanded in the inner space of the coiled anchor; and a prosthetic valve comprising an expandable frame and housing a plurality of leaflets for controlling blood flow therethrough, wherein the prosthetic valve is expandable to a width that is at least the width of the stent when the stent is expanded, such that the prosthetic valve is configured to be held in the stent.