This review discusses area laws for entanglement entropy in quantum many-body systems. Area laws describe how the entanglement entropy of a subregion scales with the boundary area of that region, rather than its volume. These laws are important in quantum information theory, black hole physics, and quantum many-body physics. The review covers results from one-dimensional and higher-dimensional systems, including bosonic and fermionic models, and discusses their implications for numerical simulations. It also addresses topics such as disordered systems, non-equilibrium dynamics, and topological entanglement entropy. The review emphasizes the connection between area laws and the efficiency of numerical simulations, particularly in the context of matrix-product states and entanglement renormalization. It also discusses the relationship between area laws and the speed of information propagation in quantum lattice models. The review concludes with a discussion of the implications of area laws for quantifying the effective degrees of freedom in quantum simulations.This review discusses area laws for entanglement entropy in quantum many-body systems. Area laws describe how the entanglement entropy of a subregion scales with the boundary area of that region, rather than its volume. These laws are important in quantum information theory, black hole physics, and quantum many-body physics. The review covers results from one-dimensional and higher-dimensional systems, including bosonic and fermionic models, and discusses their implications for numerical simulations. It also addresses topics such as disordered systems, non-equilibrium dynamics, and topological entanglement entropy. The review emphasizes the connection between area laws and the efficiency of numerical simulations, particularly in the context of matrix-product states and entanglement renormalization. It also discusses the relationship between area laws and the speed of information propagation in quantum lattice models. The review concludes with a discussion of the implications of area laws for quantifying the effective degrees of freedom in quantum simulations.