  Chern-Simons theory in the 1/N expansion has been conjectured to be
equivalent to a topological string theory. This conjecture predicts a
remarkable relationship between knot invariants and Gromov-Witten theory. We
review some basic aspects of this relationship, as well as the tests of this
conjecture performed over the last ten years. Particular attention is given to
indirect tests based on integrality conjectures, both for the HOMFLY and for
the Kauffman invariants of links.
