Kontsevich integral : state of the art The Kontsevich integral is known to be a universal Vassiliev invariant.
It is still an open question whether it is a complete knot invariant, i.e. whether it distinguishes a given knot from all other knots up to ambient isotopy and mirror image.
I am curious to know if there are some references giving the state of the art for this important question. Have some clues for a possible answer emerged in the last few years?
 A: I don't think that there has been a tremendous amount of progress in understanding the Kontsevich Invariant of a knot in the last decade or so. It appears that essential new ideas may be needed in order to answer the fundamental questions.
 Quantum Invariants: A study of knots, $3$-manifolds, and their sets, T. Ohtsuki, World Scientific 2002. This is still more-or-less current, I think, and is a basic reference. Also T. Ohtsuki's Problems on invariants of knots and 3–manifolds.

A more recent textbook reference is: Introduction to the Vassiliev Knot Invariants by Chmutov, Duzhin, and Mostovoy, Cambridge University Press, 2012. It contains a detailed discussion of the Kontsevich Invariant of a knot, including developments of the last decade such as work that has been done on the loop expansion and on the 2-loop polynomial in particular.

With regard to clues for a final answer, not to toot my own horn, but Ohtsuki and I showed that 3 loop Vassiliev invariants do not distinguish a knot from its reverse (this is trivial for lower loop degree):

Vanishing of 3-loop Jacobi diagrams of odd degree, D. Moskovich and T. Ohtsuki, J. Comb. Theory, Ser. A 114(5): 919-930 (2007).
If this were true for general loop degree, then that would imply that there exist prime unoriented knots which cannot be distinguished by the Kontsevich invariant (this is a result of Kuperberg). My personal suspicion (without solid support) is that this is false for general loop degree, and indeed that the Kontsevich invariant does separate (unoriented) knot types.
