  A brief review on the progress made in the study of Chern-Simons gauge theory
since its relation to knot theory was discovered ten years ago is presented.
Emphasis is made on the analysis of the perturbative study of the theory and
its connection to the theory of Vassiliev invariants. It is described how the
study of the quantum field theory for three different gauge fixings leads to
three different representations for Vassiliev invariants. Two of these gauge
fixings lead to well known representations: the covariant Landau gauge
corresponds to the configuration space integrals while the non-covariant
light-cone gauge to the Kontsevich integral. The progress made in the analysis
of the third gauge fixing, the non-covariant temporal gauge, is described in
detail. In this case one obtains combinatorial expressions, instead of integral
ones, for Vassiliev invariants. The approach based on this last gauge fixing
seems very promising to obtain a full combinatorial formula. We collect the
combinatorial expressions for all the Vassiliev invariants up to order four
which have been obtained in this approach.
