This review discusses the application of conformal field theory (CFT) to the calculation of entanglement entropy in 1+1 dimensions. The authors present a self-contained presentation of the results obtained using CFT, covering various aspects such as the entanglement entropy of a single interval, finite size and temperature effects, systems with boundaries, and the entanglement of disjoint intervals. They also explore the behavior away from critical points and the spectrum of the reduced density matrix. The review includes discussions on quantum quenches, which are non-equilibrium scenarios, and proposes methods for measuring entanglement entropy in real experiments. The key findings include the universal scaling of entanglement entropy at critical points, the role of the central charge, and the importance of twist fields in the calculation of entanglement entropy. The authors provide detailed mathematical derivations and numerical examples to support their arguments.This review discusses the application of conformal field theory (CFT) to the calculation of entanglement entropy in 1+1 dimensions. The authors present a self-contained presentation of the results obtained using CFT, covering various aspects such as the entanglement entropy of a single interval, finite size and temperature effects, systems with boundaries, and the entanglement of disjoint intervals. They also explore the behavior away from critical points and the spectrum of the reduced density matrix. The review includes discussions on quantum quenches, which are non-equilibrium scenarios, and proposes methods for measuring entanglement entropy in real experiments. The key findings include the universal scaling of entanglement entropy at critical points, the role of the central charge, and the importance of twist fields in the calculation of entanglement entropy. The authors provide detailed mathematical derivations and numerical examples to support their arguments.