Apparatuses and methods are disclosed for performing a procedure on a heartvalve in which a loopof material is configured to contact at least a portion of the annulus or theleaflets of a valve. A plurality ofanchors are distributed about the loop and configured for implantation intothe annulus or the leaflets in aforward direction. The anchors are configured to resist extraction in abackwards direction. A plurality oflinking members are affixed to the loop of material and at least a portion ofeach linking member passesthrough a slot in a respective anchor so that the linking members can slidewith respect to the slots. Theanchors are then implanted into the annulus or the leaflets. The loop can thenbe used to retain a replacementvalve or to cinch the annulus. A number of particularly advantageous anchorconfigurations are alsodisclosed.