Some embodiments described herein include a heart valve replacement system that may be delivered to a targeted native heart valve site via one or more delivery catheters. In some embodiments, a prosthetic heart valve of the system includes structural features that securely anchor the prosthetic heart valve to the site of the native heart valve. Such structural features can provide robust migration resistance. In particular implementations, the prosthetic heart valves occupy a smaller delivery profile, thereby facilitating a smaller delivery catheter for advancement to the heart.