Abstract:  In the last few years, C. Blanchet, F. Costantino, M. De Renzi, B. Patureau, N. Reshetikhin, V. Turaev and myself (in various collaborations) have developed a theory of renormalized quantum invariants of links and 3-manifolds which lead to TQFTs.  This talk will start out by giving an overview of this work.  In the second part of the talk I will discuss the renormalized quantum invariants of links coming from quantized $sl(2)$ at a root of unity. These link invariants contain Kashaev's quantum dilogarithm invariants of knots and the multi-variable Alexander Polynomial. This theory is also related to logarithmic conformal field theory.