Title: Topology of knot spaces in dimension 3 Abstract: I will outline some recent developments in our understanding of the homotopy type of knot spaces in dimension 3. These include results such as: The space of long knots in dimension 3 is a free little 2-cubes object. A conjectural classification of the homotopy type of the space of long knots in R^3 (or equivalently embeddings of S^1 in S^3). A homological characterization of the unknot.