We review the recent progress in the density functional theory for superconductors (SCDFT). Motivated by the long-studied plasmon mechanism of superconductivity, we have constructed an exchange-correlation kernel entering the SCDFT gap equation which includes the plasmon effect. For the case of lithium under high pressures, we show that the plasmon effect substantially enhances the transition temperature (Tc) by cooperating with the conventional phonon mechanism and results in a better agreement between the theoretical and experimentally observed Tc. Our present formalism will be a first step to density functional theory for unconventional superconductors. ; Comment: 9 pages, 7 figures; accepted for publication in J. Phys. Soc. Jpn. Special Topics; conference proceedings of The International Conference on Strongly Correlated Electron Systems (SCES) 2013