  In this chapter, we provide a review of ground-state Kohn-Sham
density-functional theory of electronic systems and some of its extensions, we
present exact expressions and constraints for the exchange and correlation
density functionals, and we discuss the main families of approximations for the
exchange-correlation energy: semilocal approximations, single-determinant
hybrid approximations, multideterminant hybrid approximations,
dispersion-corrected approximations, as well as orbital-dependent
exchange-correlation density functionals. The chapter aims at providing both a
consistent bird's-eye view of the field and a detailed description of some of
the most used approximations. It is intended to be readable by
chemists/physicists and applied mathematicians.
