Given a unitary Modular Tensor Category M, the reconstruction program asks for the construction of a rational conformal field theory such that its representation category is isomorphic to M. This is a low dimensional version of Dolpicher-Roberts/Deligne theory which is much richer due to nontrivial representations of braid group, and is strongly motivated by recent development in subfactor theory. In this talk we will describe questions around this program and present recent progress.