A pair $(X,E)$ consisting of a smooth Fano variety together with a choice of smooth anticanonical divisor corresponds under mirror symmetry to a family $W : U \rightarrow {\mathbb A}^1$ of Calabi-Yau varieties over the affine line such that the monodromy at infinity is maximally unipotent. Moreover, a degeneration of $(X,E)$ to a singular toric Fano variety together with its toric boundary corresponds to an open embedding of an algebraic torus in $U$. Using this heuristic, we construct smoothings of Gorenstein toric Fano 3-folds determined by combinatorial data encoding the construction of the mirror as a blowup of a toric variety. The smoothing is described using the scattering diagram of Kontsevich-Soibelman and Gross-Siebert which encodes counts of holomorphic discs on the mirror via tropical geometry. This is a part of a program initiated by Coates, Corti, Galkin, Golyshev, and Kasprzyk to classify smooth Fano varieties using mirror symmetry. Period and Gromov-Witten calculations by these authors suggest that all deformation types of Fano 3-folds are obtained by our construction. This is a report on work in progress with Alessio Corti, Mark Gross, and Andrea Petracci.