A mitral valve prosthesis (100A, 100B, 200, 600A, 600B) for implantation in an annulus of a native mitral valve, including a frame; an expandable outer support structure having two engagement arms and two commissure posts (108, 208); and a valve prosthesis sutured to the frame; wherein the frame comprises: a first expandable inflow region formed of a plurality of cells and configured to expand within and support against the walls of the left atrium, wherein the first expandable inflow region has a cross-sectional diameter larger than the annulus of the native mitral valve, wherein the first expandable inflow region has a non-circular cross-section to accommodate the anterior horn of the atrium; and a second expandable outflow region formed of a plurality of cells and configured to expand within and support against the native mitral valve annulus; and wherein a first end of each of the two engagement arms is coupled to one of the two commissure posts (108, 208) and a second end of each of the two engagement arms is coupled to the other one of the two commissure posts (108, 208), wherein the engagement arms are upwardly concave such as to form a trough adjacent to a throat section of the frame, and wherein a distal section of the frame is coupled to the commissure posts (108, 208) of the outer support structure; and wherein the commissural posts (108, 208) are non-diverging. a frame; an expandable outer support structure having two engagement arms and two commissure posts (108, 208); and a valve prosthesis sutured to the frame; wherein the frame comprises: a first expandable inflow region formed of a plurality of cells and configured to expand within and support against the walls of the left atrium, wherein the first expandable inflow region has a cross-sectional diameter larger than the annulus of the native mitral valve, wherein the first expandable inflow region has a non-circular cross-section to accommodate the anterior horn of the atrium; and a second expandable outflow region formed of a plurality of cells and configured to expand within and support against the native mitral valve annulus; and wherein a first end of each of the two engagement arms is coupled to one of the two commissure posts (108, 208) and a second end of each of the two engagement arms is coupled to the other one of the two commissure posts (108, 208), wherein the engagement arms are upwardly concave such as to form a trough adjacent to a throat section of the frame, and wherein a distal section of the frame is coupled to the commissure posts (108, 208) of the outer support structure; and wherein the commissural posts (108, 208) are non-diverging. a first expandable inflow region formed of a plurality of cells and configured to expand within and support against the walls of the left atrium, wherein the first expandable inflow region has a cross-sectional diameter larger than the annulus of the native mitral valve, wherein the first expandable inflow region has a non-circular cross-section to accommodate the anterior horn of the atrium; and a second expandable outflow region formed of a plurality of cells and configured to expand within and support against the native mitral valve annulus; and wherein a first end of each of the two engagement arms is coupled to one of the two commissure posts (108, 208) and a second end of each of the two engagement arms is coupled to the other one of the two commissure posts (108, 208), wherein the engagement arms are upwardly concave such as to form a trough adjacent to a throat section of the frame, and wherein a distal section of the frame is coupled to the commissure posts (108, 208) of the outer support structure; and wherein a first end of each of the two engagement arms is coupled to one of the two commissure posts (108, 208) and a second end of each of the two engagement arms is coupled to the other one of the two commissure posts (108, 208), wherein the engagement arms are upwardly concave such as to form a trough adjacent to a throat section of the frame, and wherein a distal section of the frame is coupled to the commissure posts (108, 208) of the outer support structure; and wherein the commissural posts (108, 208) are non-diverging.