Abstract: Vassiliev knot invariants can be most easily defined through a simple combinatorial axiom. Unfortunately this axiom does not give much insight into what topological information these invariants carry. In this talk I will present two new topological interpretations of these invariants. The first is joint work with Peter Teichner, which shows that these invariants form a complete set of embedding obstructions to certain 2-complexes called gropes. The second interpretation is joint work in progress with Ryan Budney, Kevin Scannell and Dev Sinha, which shows that Vassiliev invariants can be strongly related to the homotopy theory of certain topological spaces.