Density functional theory (DFT) is an in-principle exact reformulation of the quantum ground-state electronic structure problem. Derived in the mid-1960s [1,2], it is now considered as the workhorse of quantum chemistry and materials science [3]. Despite this success, which is due to the development of ever more precise (ground-state) density-functional approximations, DFT has both practical and theoretical limitations that make it a vivid field of research. In this presentation, I will discuss formal extensions of DFT to excited states. The importance of both formal exactness and practical implementation opportunities will be emphasized. As an illustration, I will discuss more specifically three extensions of DFT that are currently under development: The N-centered ensemble DFT of ionization potentials and electron affinities [4,5], beyond-Born-Oppenheimer DFT [6,7], and an extension of thermal DFT based on the concept of thermofield [8,9].

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[2] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).

[3] A. M. Teale, T. Helgaker, A. Savin, ..., E. Fromager et al., Phys. Chem. Chem. Phys. (2022) 24, 28700-28781.

[4] L. Dupuy and E. Fromager, Phys. Rev. Lett. 137, 088001 (2026).

[5] L. Dupuy, T. Chiti, J. Morere, and E. Fromager, J. Chem. Phys. 165, 030902 (2026).

[6] E. Fromager and B. Lasorne, 2024 Electron. Struct. 6 025002.

[7] L. Dupuy, B. Lasorne, and E. Fromager, Journal of Computational Chemistry 47, no. 19 (2026): e70459

[8] G. Harsha, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys. 150, 154109 (2019).

[9] G. Harsha and E. Fromager, in preparation (2026).