  This manuscript is a review of the main results obtained in a series of
papers involving the present authors and their collaborator J.L. Cardy over the
last two years. In our work we have developed and applied a new approach for
the computation of the bi-partite entanglement entropy in massive
1+1-dimensional quantum field theories. In most of our work we have considered
these theories to be also integrable. Our approach combines two main
ingredients: the "replica trick" and form factors for integrable models and
more generally for massive quantum field theory. Our basic idea for combining
fruitfully these two ingredients is that of the branch-point twist field. By
the replica trick we obtained an alternative way of expressing the entanglement
entropy as a function of the correlation functions of branch-point twist
fields. On the other hand, a generalisation of the form factor program has
allowed us to study, and in integrable cases to obtain exact expressions for,
form factors of such twist fields. By the usual decomposition of correlation
functions in an infinite series involving form factors, we obtained exact
results for the infrared behaviours of the bi-partite entanglement entropy, and
studied both its infrared and ultraviolet behaviours for different kinds of
models: with and without boundaries and backscattering, at and out of
integrability.
