Mirror symmetry is a phenomenon discovered by string theorists, which relates physical theories obtained using different deformation families of Calabi-Yau manifolds. An algebro-geometric approach to mirror symmetry, which uses tropical and log geometric tools to construct such families of Calabi-Yau manifolds, is provided by the Gross-Siebert program. In this talk we will review the most recent advances in this program, and particularly report on our joint work with Mark Gross.