The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations

This survey article begins with a discussion of the original form of the Strominger-Yau-Zaslow conjecture, surveys the state of knowledge concering this conjecture, and explains how thinking about this conjecture naturally leads to the program initiated by the author and Bernd Siebert to study mirror symmetry via degenerations of Calabi-Yau manifolds and log structures.