In this talk I will review some of the work on Entanglement Entropy that I have carried out in collaboration with various authors since 2007. For general 1d Quantum Field Theories, the central objects are Twist Fields whose correlation functions are directly related to the entropy. In the context of Quantum Spin Chains, Twist Operators play a similar role and products thereof can be related to the twist fields in the continuous limit.
Once the entropy has been expressed in terms of correlation functions of these fields (or operators on the chain) one may exploit the powerful tools of integrable quantum models to establish new results. We may study both the short- and long-distance behaviours of the entropy in various kinds of theories, study the matrix elements of twist fields (or twist operators) on their own right, or investigate the features of other correlation functions involving the twist field. In my talk I will try to touch on the main results we have obtained when addressing some of these problems.
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