Abstract: 

In this talk I will recall the volume conjectures of various 3-manifold invari.ants constructed from TOFTs, including the colored Jones polynomials (Kashaev.Murakami-Murakami), the Reshetikhin-Turaev and the Turaev-Viro invariants (ChenYang) and their relative versions, and introduce some of the recent progresses.