This chapter delves into theoretical methods of electronic structure, which is the basis to simulate a real condensed matter system accurately at the quantum-mechanical level. It begins with an overview of the history of full quantum theory, which describes the quantum properties of nucleus, electron and their quantum coupling. Beyond the Born–Oppenheimer approximation, Born–Huang expansion is introduced which expands the system as a sum over electron–nuclear wavefunction products. It is a rigorous approach describing electron–phonon coupling and is believed to become the dominant paradigm in condensed matter physics with the rapid improvement of simulation and high-resolved experimental techniques. History, theoretical framework, and challenges of the mainstream electronic structure calculation methods are introduced. These include wavefunction method (Hartree method, Hartree–Fock method, and post-Hartree–Fock method), density functional theory (DFT), and Quantum Monte Carlo Method (QMC). The accuracy of post-Hartree–Fock methods (consider dynamical correlation of electron) makes them remain important while DFT is the most common method in physics, chemistry and material, being important foundation of full-quantum calculation. The impact of QMC keeps increasing in computational physics due to its adaptation to supercomputers. Then, the method for excited electronic state calculation is introduced, which is also needed in full quantum calculation. The GW Method is recommended because it can treat the quasiparticle–electron excitation properties accurately. Finally, the chapter introduces current realizations of electronic-structure calculation and their challenges (e.g., balance between accuracy and efficiency). It discusses key concepts such as basis set, pseudopotential, and boundary condition. The associated programs are summarized.