A mitral valve replacement system for a heart, comprising: an expandable anchor assembly configured to implant at a native mitral valve, the expandable anchor assembly including an expandable anchor frame that is adjustable from a delivery condition to an expanded condition; an anchor delivery sheath having a distal end insertable into a left atrium and being configured to express the anchor assembly out from the distal end such that the anchor assembly expands within the left atrium to the expanded condition; a pusher instrument releasably attachable to the expandable anchor frame and being configured to longitudinally advance the anchor assembly within the left atrium towards an annulus of the native mitral valve while the anchor assembly is in the expanded condition; and an artificial valve assembly comprising an expandable valve frame that is adjustable from a compressed condition to a deployed condition to selectively engage with the anchor assembly while the anchor assembly is in the expanded condition; characterized in that the anchor assembly comprises a set of sub-annular anchor feet configured to engage with a sub-annular gutter of the native mitral valve; the expandable anchor frame includes a hub and two or more sub-annular support arms extending from the hub, wherein each of the two or more sub-annular support arms extend to the anchor feet, and supra-annular structures including anchor arches joined with each other to form an undulating supra-annular ring that acts as a supra-annular structural element for the anchor assembly, connection bridges , and including atrial holding features configured to contact the shelf-like supra-annular tissue surface above the mitral valve annulus, and to thereby stabilize the anchor assembly in supra-annular areas that are generally opposite of the anchor feet . an expandable anchor assembly configured to implant at a native mitral valve, the expandable anchor assembly including an expandable anchor frame that is adjustable from a delivery condition to an expanded condition; an anchor delivery sheath having a distal end insertable into a left atrium and being configured to express the anchor assembly out from the distal end such that the anchor assembly expands within the left atrium to the expanded condition; a pusher instrument releasably attachable to the expandable anchor frame and being configured to longitudinally advance the anchor assembly within the left atrium towards an annulus of the native mitral valve while the anchor assembly is in the expanded condition; and an artificial valve assembly comprising an expandable valve frame that is adjustable from a compressed condition to a deployed condition to selectively engage with the anchor assembly while the anchor assembly is in the expanded condition; characterized in that the anchor assembly comprises a set of sub-annular anchor feet configured to engage with a sub-annular gutter of the native mitral valve; the expandable anchor frame includes a hub and two or more sub-annular support arms extending from the hub, wherein each of the two or more sub-annular support arms extend to the anchor feet, and supra-annular structures including anchor arches joined with each other to form an undulating supra-annular ring that acts as a supra-annular structural element for the anchor assembly, connection bridges , and including atrial holding features configured to contact the shelf-like supra-annular tissue surface above the mitral valve annulus, and to thereby stabilize the anchor assembly in supra-annular areas that are generally opposite of the anchor feet . <EOS>