  Recent progress in the field of (time-independent) ensemble
density-functional theory (DFT) for excited states are reviewed. Both
Gross-Oliveira-Kohn (GOK) and $N$-centered ensemble formalisms, which are
mathematically very similar and allow for an in-principle-exact description of
neutral and charged electronic excitations, respectively, are discussed. Key
exact results like, for example, the equivalence between the infamous
derivative discontinuity problem and the description of weight dependencies in
the ensemble exchange-correlation density functional, are highlighted. The
variational evaluation of orbital-dependent ensemble Hartree-exchange (Hx)
energies is discussed in detail. We show in passing that state-averaging
individual exact Hx energies can lead to severe (solvable though)
$v$-representability issues. Finally, we explore the possibility to use the
concept of density-driven correlation, which has been recently introduced and
does not exist in regular ground-state DFT, for improving state-of-the-art
correlation density-functional approximations for ensembles. The present review
reflects the efforts of a growing community to turn ensemble DFT into a
rigorous and reliable low-cost computational method for excited states. We hope
that, in the near future, this contribution will stimulate new formal and
practical developments in the field.
