In this seminar we will review several aspects of the entanglement entropy in homogeneous and quadratic fermionic chains with long-range couplings. Employing some novel results that we have found for determinants of block Toeplitz matrices, we can obtain analytically the asymptotic behavior of the entanglement entropy, both for a single interval of the chain and for several disjoint intervals. We have applied these general techniques in several particular systems such as the XY spin chain, fermionic ladders and long-range Kitaev chains, unraveling new regimes of the entanglement entropy. Our investigation has also led us to discover a new symmetry of the entanglement entropy under Möbius transformations that can be interpreted as transformations in the couplings of the theory. This symmetry establishes a connection between the ground states of different Hamiltonians that are not related by unitary transformations. In addition, there is an intriguing parallelism between this symmetry and conformal transformations in real space.