After a short review on a few "classic" results concerning the entanglement (Von Neumann) entropy in quantum lattice models (boundary law, spin chains, etc.), I will explain how this knowledge has helped to design efficient methods to numerically store and compute many-body wave functions (tensor product states). Next, I will present some numerical and analytical results concerning universal constants in the entanglement entropy of some particular 2D quantum critical states (J.-M. Stéphan et al., arXiv 0906.1153). We considered in particular the so-called "Rokhsar Kivelson" (RK) states for dimers on the square and honeycomb lattices. These calculations were made possible by the observation that, in such particular 2D wave functions, the entanglement entropy of a half-infinite cylinder is given by the configuration (or Shannon) entropy of the (1D) ground-state of the associated classical transfer matrix. Some applications to quantum spin chains will also be presented.