This article summarizes basic aspects of time‐dependent density functional theory (TD‐DFT) and its applications in inorganic chemistry. Sections titled TD‐DFT and Spectroscopic Properties outline some of the theoretical formalism and explain how excitation energies can be obtained from TD‐DFT linear response theory. Common approximations in density functional theory (DFT) exchange‐correlation (XC) potentials that might have adverse effects on the accuracy of computed results are explained. Sections titled Benchmark Data and Some Case Studies discuss a number of case studies, with emphasis on TD‐DFT excitation spectra computations in coordination chemistry. Computations of spectra and other properties of metals clusters are also discussed. Apart from excitation spectra, this section also describes TD‐DFT computations of Raman intensities (including resonance Raman and surface‐enhanced Raman spectra (SERS)), magnetic circular dichroism, optical rotatory dispersion (CD and ORD), and concludes with some comments on relativistic effects.