  Duality symmetries for strings moving in non-trivial spacetime backgrounds
are analysed. It is shown that, for backgrounds generated from compact WZW and
coset models, such duality symmetries are exact to all orders in string
perturbation theory. A global treatment of duality symmetries is given, by
associating them to the known symmetries of affine current algebras
(affine-Weyl group and external automorphisms). It is argued that self-duality
symmetries of WZW and coset models generate the duality symmetries of their
moduli space. Some remarks are presented, concerning the survival of such
symmetries in the non-compact case. The implications of duality symmetries for
string dynamics in non-trivial/singular spacetimes are discussed. (Talk given
at the "Strings 93" Conference at Berkeley, May 1993)
