This review presents the conformal field theory (CFT) approach to entanglement entropy in one-dimensional (1D) systems. It discusses the calculation of entanglement entropy for a single interval, generalizations to finite temperature, finite size, and systems with boundaries, as well as the case of multiple disjoint intervals. The paper also covers non-critical models, the entanglement spectrum, and quantum quenches. The central result is the universal scaling of entanglement entropy at critical points, given by $ S_A = \frac{c}{3} \ln \frac{\ell}{a} + c_1' $, where $ c $ is the central charge, $ \ell $ is the length of the interval, and $ a $ is the short-distance cutoff. The paper also discusses the behavior of entanglement entropy away from critical points, the spectrum of the reduced density matrix, and the role of entanglement in non-equilibrium situations. It highlights the importance of CFT in understanding entanglement in many-body systems and provides a comprehensive overview of the current state of research in this area.This review presents the conformal field theory (CFT) approach to entanglement entropy in one-dimensional (1D) systems. It discusses the calculation of entanglement entropy for a single interval, generalizations to finite temperature, finite size, and systems with boundaries, as well as the case of multiple disjoint intervals. The paper also covers non-critical models, the entanglement spectrum, and quantum quenches. The central result is the universal scaling of entanglement entropy at critical points, given by $ S_A = \frac{c}{3} \ln \frac{\ell}{a} + c_1' $, where $ c $ is the central charge, $ \ell $ is the length of the interval, and $ a $ is the short-distance cutoff. The paper also discusses the behavior of entanglement entropy away from critical points, the spectrum of the reduced density matrix, and the role of entanglement in non-equilibrium situations. It highlights the importance of CFT in understanding entanglement in many-body systems and provides a comprehensive overview of the current state of research in this area.