Abstract
We review some recent advances in the computation of exact correlation functions of the XXZ-1/ 2 Heisenberg chain. We first give a general introduction to our method which is based on the algebraic Bethe ansatz and the resolution of the quantum inverse scattering problem, leading in particular to multiple integral representations for the correlation functions. Then we describe recently obtained compact formulas for the spin-spin correlation functions of the XXZ-1/ 2 Heisenberg chain. We outline how this leads to several explicit results including the known two point functions in the limit of free fermions, the so-called emptiness formation probability at anisotropy $Delta=1/2$ and its large distance asymptotic behavior in the massless phase of the model.