CXs can be appropriately described using a variety of (mostly multireference) electronic structure methods, but the present chapter focuses on their description using time-dependent density functional theory (TDDFT) in its linear-response (LR) formulation. The frequency-domain formulation of LR-TDDFT involves an eigenvalue problem for the excitation energies and no explicit time dependence, nevertheless that method is nowadays largely synonymous with simply "TDDFT". Explicitly time-dependent approaches do exist and their use is increasing, 15 but these are not discussed in the present chapter. LR-TDDFT represents something of a "sweet spot" in terms of its price-to-performance ratio, with an accuracy of ∼ 0.3 eV for many classes of vertical excitation energies, and a cost that scales as n states × O(n 4 basis ), i.e., fourthorder scaling with a prefactor that reflects the number of desired states. For many photochemical problems, only a few low-lying electronic states are required and the cost is not significantly greater than that of the ground-state DFT calculation.