(1.2) In recent years, much progress has been made, in particular by Kontsevich–Soibelman [KS00, KS06] and Gross–Siebert [GS11a]. Both of these programs are based on a conjectural geometric explanation of mirror symmetry due to Strominger, Yau and Zaslow, known as the SYZ conjecture [SYZ96]. Since its appearance, the conjecture has been amended in certain ways; a common way to formulate it today is the following. Let $\mathcal{X}^{\ast}$ be a projective family of $n$-dimensional complex Calabi-Yau varieties over a punctured disk $\Delta^{\ast}$, and assume that this family is maximally degenerate. The latter condition means that the monodromy transformation on the degree $n$ cohomology of the general fiber $\mathcal{X}_{t}$ of $\mathcal{X}^{\ast}$ has a Jordan block of rank $n+1$. Then, up to rescaling the metrics, the family $\mathcal{X}_{t}$ is conjectured to converge in the Gromov-Hausdorff limit to an $n$-dimensional topological manifold $S$. Moreover, a general fiber $\mathcal{X}_{t}$ should admit a fibration $\rho\colon\mathcal{X}_{t}\to S$, called an SYZ fibration, whose fibers are special Lagrangian tori in $\mathcal{X}_{t}$, except over a discriminant locus of codimension at least $2$ in the base $S$. The mirror partner of $\mathcal{X}_{t}$ can then be constructed by dualizing the torus fibration $\rho$ over the smooth locus and compactifying the result in an appropriate way (this involves deforming the dual fibration by so-called quantum corrections). We refer to the excellent survey paper [Gr13] for a more precise statement and additional background on the SYZ conjecture, as well as the Gross–Siebert program.