The density-matrix renormalization group (DMRG) is a numerical algorithm designed to efficiently truncate the Hilbert space of low-dimensional strongly correlated quantum systems. It has achieved unprecedented precision in describing one-dimensional quantum systems and has become a standard tool for studying such systems. The review covers the key aspects of DMRG, including real-space renormalization of Hamiltonians, density matrices, infinite-system DMRG, finite-system DMRG, symmetries, and the calculation of energies. It also discusses the application of DMRG to various fields, such as two-dimensional quantum systems, quantum chemistry, and statistical physics. The theoretical foundations of DMRG, including its relationship to matrix-product states and quantum information theory, are explored. The review highlights the versatility and precision of DMRG, while also addressing its limitations, particularly in higher dimensions.The density-matrix renormalization group (DMRG) is a numerical algorithm designed to efficiently truncate the Hilbert space of low-dimensional strongly correlated quantum systems. It has achieved unprecedented precision in describing one-dimensional quantum systems and has become a standard tool for studying such systems. The review covers the key aspects of DMRG, including real-space renormalization of Hamiltonians, density matrices, infinite-system DMRG, finite-system DMRG, symmetries, and the calculation of energies. It also discusses the application of DMRG to various fields, such as two-dimensional quantum systems, quantum chemistry, and statistical physics. The theoretical foundations of DMRG, including its relationship to matrix-product states and quantum information theory, are explored. The review highlights the versatility and precision of DMRG, while also addressing its limitations, particularly in higher dimensions.