  We review the relation between Chern-Simons gauge theory and topological
string theory on noncompact Calabi-Yau spaces. This relation has made possible
to give an exact solution of topological string theory on these spaces to all
orders in the string coupling constant. We focus on the construction of this
solution, which is encoded in the topological vertex, and we emphasize the
implications of the physics of string/gauge theory duality for knot theory and
for the geometry of Calabi-Yau manifolds.
