The progress of experimental techniques makes more and more precise measurements available. Their interpretation requires improved theoretical tools. The time-dependent density functional theory (TDDFT) allows to study electronic excitations involved in spectroscopic experiments, possibly conserving a computational effort comparable to that of ground-state density functional theory. I will present some applications of TDDFT to the calculation of absorption and electron energy loss spectra in extended and finite systems, discussing the advantages and the limits of different approximation schemes.