In this talk I will present a short review on the algebraic Bethe ansatz technique and on the recently found solution of the so-called inverse problem. I will show how this solution provides a means for the explicit and exact computation of correlation functions in spin chains and summarize some of the many results obtained in this direction by members of the theory group at the ENS-Lyon in the last years. Finally I will present some work still in progress which intends the generalization of these techniques to the case of spin chains in the presence of impurities.