Prosthetic heart valve apparatus is adapted for delivery into a patient in a circumferentially collapsed condition, followed by circumferential re-expansion at the implant site in the patient. The apparatus includes an annular anchoring structure that can be implanted in the patient first. The apparatus further includes an annular valve support structure, which supports a flexible leaflet structure of the valve. The support and leaflet structures are initially separate from the anchoring structure, but they can be implanted in the patient by interengagement of the support structure with the already-implanted anchoring structure.