Recent years have seen an extraordinary development in the applicability and accuracy of ab initio methods to compute molecular excited states, which are now generally determined with a precision of 0.1–0.2 eV. The size and character of the problems have increased to make the calculations competitive and complementary to the experimental determinations involving medium and large molecular systems. Many examples can be provided of this new era in the quantum chemistry of the excited state where the multiconfigurational methods, in particular, CASPT2, have been the main protagonists. The present article contains an account of the types and nature of excited states, a compilation of methods, strategies, and problems to be solved in the calculation of molecular excited states, particularly to obtain electronic transition energies and properties, such as band intensities and state lifetimes. Finally, a number of examples and achievements in the field give an overall view of what can be computed nowadays and how the computations can be performed. Illustrative examples include the calculation of dark states, vibrational resolution of electronic bands, novel assignments, interplay between theoretical spectroscopy and experiment, and adiabatic and nonadiabatic photochemical processes.