Expandable heart valves for minimally invasive valve replacement surgeries are disclosed. The valves are rolled into a first, contracted configuration for minimally invasive delivery and then unrolled or unfurled at the implantation site. One- and two-piece stents may be used in conjunction with a plurality of flexible leaflet-forming membranes. The one-piece stents may include an annulus anchoring section, a sinus section with the membranes attached over sinus apertures, and a rigid outflow section. The two-piece stent may include a primary stent to provide a tubular base at the annulus, and a secondary stent having the membranes that couples within the primary stent. Lockout tabs to secure the stents in their expanded shapes are provided. Also, alignment structure may be provided to ensure concentric unfurling. Anchoring barbs at the stent edges or in the stent body secure the valve within the annulus. Methods of implantation are also provided.