A gentle introduction to the 3d/3d correspondence

In this talk, I will survey the development of the 3d/3d correspondence in the past years. The 3d/3d correspondence is the duality between complex Chern-Simons theory on a 3-manifold and 3d N=2 theory labeled by the 3-manifold. Although the full picture is yet to be uncovered, it exhibits a spectacular interplay between topology of 3-manifolds and QFT. In this talk, I introduce established examples such as modular transformations, equivariant Verlinde formulas, Z-hat, and quantum modularity in the 3d/3d correspondence. I will also mention open problems in this area.