The orbital energies for the frontier HOMO and LUMO have been rigorously shown to be the DFA prediction of the negative of the first IP and the first electron affinity (EA) in 2008. Three key results were used in the proof. (1) The Janak theorem shows that KS orbital energies are the derivatives of the total energy with respect to the orbital occupation numbers. Note that the Janak theorem does not relate orbital energies to any physical observables. (2) The left and right derivatives of the total energy with respect to the total electron number, or the left and right chemical potentials, are the negative of the first IP and the first EA respectively of the corresponding energy functional. This follows from the linear condition on the behaviour of the total energy for fractional number of electrons. The linearity condition is true for the exact functional, or for a functional without delocalization error for general systems. For infinite bulk systems, however, the linearity condition holds true for any functional approximation. (3) The chemical potentials were proved to be the derivatives of the energy with respect to the orbital occupation numbers of HOMO and LUMO in a Kohn-Sham calculation, when the exchange-correlation energy used is a functional of the density. With the use of the Janak theorem, this then es-tablishes that the KS HOMO and LUMO energies are the chemical potentials of the system for the given DFA. Similarly, when the exchange-correlation energy is a functional of the noninteracting one-electron density matrix, the chemical potentials were proved to be the derivatives of the energy with respect to the orbital occupation numbers of HOMO and LUMO in a generalized Kohn-Sham calculation. Therefore, the HOMO and LUMO orbital energies are the DFA prediction of the negative of the first IP and the first EA. This interpretation of the HOMO and LUMO energies holds true for molecular and bulk systems, for any given DFA.