Some open questions in TDDFT: Clues from lattice models and Kadanoff-Baym dynamics

► Lattice models to examine linear response scheme and ALDA in TDDFT. ► Linear response, lattice TDDFT, Green's function methods reviewed. ► Small clusters show drawback of TDDFT linear response; prescription to amend it. ► Limitations of ALDA in 3D Hubbard systems: linear and non-linear regime.