Several basic time-independent density-functional theorems are reviewed for ground states and excited states. In particular, the simple constrained-search formulation is utilized to prove the Hohenberg-Kohn theorem for degenerate as well as for non-degenerate situations. Then, a time-independent Kohn-Sham theory is presented for an individual excited state, and first-order adiabatic connection perturbation theory is compared with a common approximation within time-dependent theory for excited states. ©2001 American Institute of Physics.