A device for treating a mitral or tricuspid valve, comprising: a prosthetic sealing element having an elongated cross-sectional profile, the sealing element dimensioned to be deployed in an annulus of a native mitral or tricuspid valve of a heart at a position between native mitral or tricuspid valve leaflets (42a, 42p) to contact the native mitral or tricuspid valve leaflets during ventricular systole to create a seal to prevent regurgitation of blood from the left or right ventricle to the left or right atrium, wherein the sealing element is further dimensioned to permit the native mitral or tricuspid valve leaflets (42a, 42p) to open and close as the heart beats; and an anchoring element adapted for deployment in the heart, the anchoring element coupled to the sealing element, the anchoring element comprising an upper portion configured to extend around the mitral or tricuspid valve annulus and contact atrial tissue, a lower portion configured to extend around the native mitral or tricuspid valve leaflets (42a, 42p) and engage ventricular tissue while permitting opening and closing of the native mitral or tricuspid valve leaflets (42a, 42p), and a central portion configured to support the sealing element at the position between native mitral or tricuspid valve leaflets (42a, 42p), wherein the anchoring element is dimensioned to position the sealing element between the native mitral or tricuspid valve leaflets (42a, 42p) when the anchoring element is deployed in the heart; wherein the anchoring element lower portion comprises an anterior arm extending in a first direction, the anterior arm curving up from a bottom of the anchoring element toward a top of the anchoring element, wherein the anchoring element further comprises a posterior arm extending in a second direction, wherein the second direction is opposite to the first direction, the posterior arm curving up from a bottom of the anchoring element toward a top of the anchoring element; and wherein, when the device is deployed in the native mitral or tricuspid valve, the anterior arm and the posterior arm are positioned just below the native mitral or tricuspid annulus and the upper portion of the anchoring element is positioned just above the native mitral or tricuspid annulus such that the native mitral or tricuspid annulus is compressed between the arms (66a, 66p) and the upper portion of the anchoring element to thereby secure the anchoring element during ventricular systole and during ventricular diastole. a prosthetic sealing element having an elongated cross-sectional profile, the sealing element dimensioned to be deployed in an annulus of a native mitral or tricuspid valve of a heart at a position between native mitral or tricuspid valve leaflets (42a, 42p) to contact the native mitral or tricuspid valve leaflets during ventricular systole to create a seal to prevent regurgitation of blood from the left or right ventricle to the left or right atrium, wherein the sealing element is further dimensioned to permit the native mitral or tricuspid valve leaflets (42a, 42p) to open and close as the heart beats; and an anchoring element adapted for deployment in the heart, the anchoring element coupled to the sealing element, the anchoring element comprising an upper portion configured to extend around the mitral or tricuspid valve annulus and contact atrial tissue, a lower portion configured to extend around the native mitral or tricuspid valve leaflets (42a, 42p) and engage ventricular tissue while permitting opening and closing of the native mitral or tricuspid valve leaflets (42a, 42p), and a central portion configured to support the sealing element at the position between native mitral or tricuspid valve leaflets (42a, 42p), wherein the anchoring element is dimensioned to position the sealing element between the native mitral or tricuspid valve leaflets (42a, 42p) when the anchoring element is deployed in the heart; wherein the anchoring element lower portion comprises an anterior arm extending in a first direction, the anterior arm curving up from a bottom of the anchoring element toward a top of the anchoring element, wherein the anchoring element further comprises a posterior arm extending in a second direction, wherein the second direction is opposite to the first direction, the posterior arm curving up from a bottom of the anchoring element toward a top of the anchoring element; and wherein, when the device is deployed in the native mitral or tricuspid valve, the anterior arm and the posterior arm are positioned just below the native mitral or tricuspid annulus and the upper portion of the anchoring element is positioned just above the native mitral or tricuspid annulus such that the native mitral or tricuspid annulus is compressed between the arms (66a, 66p) and the upper portion of the anchoring element to thereby secure the anchoring element during ventricular systole and during ventricular diastole.