An overview of density-functional theory (DFT) is presented, which provides the basis for subsequent calculations of X-ray absorption spectra in solids. The advantages of DFT, such as the possibility of obtaining reliable atomic and electronic structures of even fairly complicated materials, as well as its disadvantages, namely the limited accuracy for certain systems containing strongly correlated electrons or having important van der Waals bonding effects and its restriction to being a ground-state theory, are discussed. The most important band-structure methods and the corresponding codes which are currently in use are then briefly reviewed, followed by an introduction to the basic theory of X-ray absorption near-edge structure. Finally, the most common methods used to include the important electron–hole interactions, namely a static core-hole approach with a supercell of the solution of the Bethe–Salpeter equation, are reviewed and selected examples from the literature using various codes are given.