Formation of metal-semiconductor core-shell heterostructures with precise morphological control of both components remains challenging. Heterojunctions, rather than core-shell structures, were typically produced for metal-semiconductor composites. Furthermore, growth of semiconductor shells with systematic shape evolution using the same metal particle cores can also present a significant challenge. Here, we have synthesized Au-Cu2O core-shell heterostructures using gold nanoplates, nanorods, octahedra, and highly faceted nanoparticles as the structure-directing cores for the overgrowth of Cu2O shells by a facile aqueous solution approach. The gold nanoparticle cores guide the growth of Cu2O shells with morphological and orientation control. Systematic shape evolution of the shells can be easily achieved by simply adjusting the volume of reductant added. For example, truncated cubic to octahedral Cu2O shells were produced from octahedral gold nanocrystal cores. Unusual truncated stellated icosahedral and star column structures have also been synthesized. The heterostructures were found to be formed via an unusual hollow-shell-refilled growth mechanism not reported before. The approach has potential toward the preparation of other complex Cu2O structures with well-defined facets.