Classifying Del Pezzo Surfaces with Mirror Symmetry

I will give an overview/recent history of techniques to classify Fano Surfaces which admit Toric Degenerations up to qG-deformation with Mirror Symmetry techniques, and how this connects with other mirror symmetry constructions such as the Gross-Siebert program. This is a nice story which relates computing enumerative invariants of Fano varieties (Harder!) with certain periods of Laurent polynomials (Easier!). If time permits, I may talk about how I'm attempting to say something about the singular case, where we now are talking about Orbifold invariants of stacks.