Described herein are methods and apparatus for implanting grafts to leaflets for cardiac procedures that are performed minimally-invasively while the heart is beating. The graft elongates, reinforces, and patches the leaflet. In certain disclosed examples, the graft is secured to the atrium or ventricle side of the leaflet with an artificial cord implanted on an edge of the graft to improve coaptation. In some disclosed examples, the graft is secured to both leaflets to enable an edge-to-edge procedure similar to the Alfieri technique. Some examples of the disclosed methods including introducing the graft into the ventricle and guiding it into place using artificial cords previously implanted in the leaflet.