  We review the Kohno-Drinfeld theorem as well as a conjectural analogue
relating quantum Weyl groups to the monodromy of a flat connection D on the
Cartan subalgebra of a complex, semi-simple Lie algebra g with poles on the
root hyperplanes and values in any g-module V. We sketch our proof of this
conjecture when g=sl(n) and when g is arbitrary and V is a vector, spin or
adjoint representation. We also establish a precise link between the connection
D and Cherednik's generalisation of the KZ connection to finite reflection
groups.
