The approaches of Givental and of Lian-Liu-Yau are formally independent of the conjectural picture of whether three-dimensional Calabi-Yau manifolds can in fact be grouped as physicists claim. With Andrew Strominger and Eric Zaslow, Yau proposed a geometric picture of how this grouping might be systematically understood. The essential idea is that a Calabi-Yau manifold with complex dimension three should be foliated by "special Lagrangian" tori, which are certain types of three-dimensional minimal submanifolds of the six-dimensional Riemannian manifold underlying the Calabi-Yau structure. Given one three-dimensional Calabi-Yau manifold, one constructs its "mirror" by looking its torus foliation, dualizing each torus, and reconstructing the three-dimensional Calabi-Yau manifold, which will now have a new structure.