  This survey was written for the Current Developments in Mathematics
conference, 2012, and is an updating of my article "The Strominger-Yau-Zaslow
conjecture: From torus fibrations to degenerations," in the Seattle 2005
proceedings. We trace progress and thinking about the SYZ conjecture since its
introduction in 1996. We begin with the original differential geometric
conjecture and its refinements, and explain how it led to the algebro-geometric
program developed by myself and Siebert. After explaining the overall
philosophy, I explain how recent results fit into this program.
