After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to extended systems and show that close to a quantum phase transition it has universal features which serve as a diagnostic of such phenomena. I discuss in details the results for the block entanglement entropy derived from conformal field theory, which describes 1+1 dimensional gapless models. Finally, I review some recent developments with particular emphasis on open problems and possible directions of research.

Universita di Pisa, Italie