In this chapter, time-dependent density functional theory is introduced and an outline of the Runge-Gross theorem is presented. An equation for linear response within time-dependent density functional theory is derived. A key ingredient of this equation is the exchange-correlation kernel for which several modern-day approximation exist. These approximations are investigatead for their ability to capture the excitonic physics in absorption and electron loss spectra. To this end, results for medium (Si and diamond) to large (LiF and Ar) band-gap insulators are presented, which exhibit excitonic physics to varying degrees.