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?



Kontsevich integral : state of the art
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](http://books.google.com.sg/books/about/Quantum_Invariants.html?id=_62ePy9Tv2MC&redir_esc=y), 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](http://www.msp.warwick.ac.uk/gtm/2002/04/p024.xhtml).


A more recent textbook reference is: 
> [Introduction to the Vassiliev Knot Invariants](http://www.google.com.sg/url?sa=t&rct=j&q=&esrc=s&frm=1&source=web&cd=2&cad=rja&ved=0CDUQFjAB&url=http%3A%2F%2Fwww.cambridge.org%2F9781107020832&ei=gXVXUsrOO4fJrAeMhICQBg&usg=AFQjCNEp_EVKrz4hqBIvwQ_852zcm92Sqg&bvm=bv.53899372,d.bmk) 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](http://www.google.com.sg/url?sa=t&rct=j&q=&esrc=s&frm=1&source=web&cd=8&cad=rja&ved=0CE8QFjAH&url=http%3A%2F%2Farxiv.org%2Fabs%2Fmath%2F0511602&ei=rnlXUv49ifusB76dgPgD&usg=AFQjCNELPlTPJIHLbxP_YE7SWI9g4RIRFw), 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](http://arxiv.org/pdf/q-alg/9712048v1.pdf)). 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.


