  We find and propose an explanation for a large variety of modularity-related
symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$
theories where such structures a priori are not manifest. These modular
structures include: mock modular forms, $SL(2,\mathbb{Z})$ Weil
representations, quantum modular forms, non-semisimple modular tensor
categories, and chiral algebras of logarithmic CFTs.
