In this talk I will review some of the main results of my research in this area, which stated in 2007 in collaboration with John L. Cardy and Benjamin Doyon. I will emphasise how a special type of field we have named branch point twist field has become an essential tool for performing computations of the entanglement entropy in non-critical systems. I will show how the relationship between correlators of twist fields and entanglement entropy allows us to recover well-known results for critical systems but also to predict new results for theories with a finite correlation length. Time permitting, I will mention some more recent results extending our understanding to non-unitary critical and non-critical systems.