By placing D3-brane as a probe at the tip of the Calabi-Yau cone, we have a 4-dimensional superconformal field theory on that D3-brane. Understanding which Calabi-Yau corresponds to which gauge theory is an important problem, especially in light of AdS/CFT correspondence. The case when Calabi-Yau is toric is analyzed most extensively, and it is long believed that the gauge theory in question is quiver gauge theory. However, converting fan to quiver and vice versa has been a difficult problem in practice. Recently, Hanany and collaborators have come up with an ingenious method to do just that, using the notion of brane tilings. We explain their algorithm, and also discuss the relation with mirror symmetry and our recent work of proving homological mirror symmetry using brane tilings and "alga" maps. (This talk is based on work with Kazushi Ueda (Osaka).)